If cosθ + cos^2 θ = 1, then sin^12 θ + 3 sin^10 θ + 3 sin^8 θ+ sin^6 θ + 2 sin^4 θ + 2 sin^2 θ – 2 =?

7,559 results

  1. tigonometry

    expres the following as sums and differences of sines or cosines cos8t * sin2t sin(a+b) = sin(a)cos(b) + cos(a)sin(b) replacing by by -b and using that cos(-b)= cos(b) sin(-b)= -sin(b) gives: sin(a-b) = sin(a)cos(b) - cos(a)sin(b) Add the two equations: sin(a+b) + sin(a-b) = ...
  2. TRIG!

    Posted by hayden on Monday, February 23, 2009 at 4:05pm. sin^6 x + cos^6 x=1 - (3/4)sin^2 2x work on one side only! Responses Trig please help! - Reiny, Monday, February 23, 2009 at 4:27pm LS looks like the sum of cubes sin^6 x + cos^6 x = (sin^2x)^3 + (cos^2x)^3 = (sin^2x+cos...
  3. algebra

    Can someone please help me do this problem? That would be great! Simplify the expression: sin theta + cos theta * cot theta I'll use A for theta. Cot A = sin A / cos A Therefore: sin A + (cos A * sin A / cos A) = sin A + sin A = 2 sin A I hope this will help. in my algebra ...
  4. Mathematics - Trigonometric Identities

    Let y represent theta Prove: 1 + 1/tan^2y = 1/sin^2y My Answer: LS: = 1 + 1/tan^2y = (sin^2y + cos^2y) + 1 /(sin^2y/cos^2y) = (sin^2y + cos^2y) + 1 x (cos^2y/sin^2y) = (sin^2y + cos^2y) + (sin^2y + cos^2y) (cos^2y/sin^2y) = (sin^2y + cos^2y) + (sin^2y + cos^2y)(sin^2y) / (sin^...
  5. math;)

    Show that sin(x+pi)=-sinx. So far, I used the sum formula for sin which is sin(a+b)=sin a cos b+cos a sin b. sin(x+pi)=sin x cos pi+cos x sin pi I think I am supposed to do this next, but I am not sure. sin(x+pi)=sin x cos x+sin pi cos pi If that is right then I am not sure ...
  6. Trigonometry

    Solve the equation for solutions in the interval 0<=theta<2pi Problem 1. 3cot^2-4csc=1 My attempt: 3(cos^2/sin^2)-4/sin=1 3(cos^2/sin^2) - 4sin/sin^2 = 1 3cos^2 -4sin =sin^2 3cos^2-(1-cos^2) =4sin 4cos^2 -1 =4sin Cos^2 - sin=1/4 (1-sin^2) - sin =1/4 -Sin^2 - sin =-3/4 ...
  7. trig

    Reduce the following to the sine or cosine of one angle: (i) sin145*cos75 - cos145*sin75 (ii) cos35*cos15 - sin35*sin15 Use the formulae: sin(a+b)= sin(a) cos(b) + cos(a)sin(b) and cos(a+b)= cos(a)cos(b) - sin(a)sin)(b) (1)The quantity = sin(145-75) = sin 70 = cos 20 note that...
  8. math

    Eliminate the parameter (What does that mean?) and write a rectangular equation for (could it be [t^2 + 3][2t]?) x= t^2 + 3 y = 2t Without a calculator (how can I do that?), determine the exact value of each expression. cos(Sin^-1 1/2) Sin^-1 (sin 7pi/6) x= t^2 + 3 y = 2t ...
  9. Trig

    Find sin(s+t) and (s-t) if cos(s)= 1/5 and sin(t) = 3/5 and s and t are in quadrant 1. =Sin(s)cos(t) + Cos(s)Sin(t) =Sin(1/5)Cos(3/5) + Cos(-1/5)Sin(3/5) = 0.389418 Sin(s-t) =sin(s)cos(t) - cos(s)sin(t) =sin(-3/5)cos(1/5) - cos(1/5)sin(3/5) =Sin-3/5 cos-3/5 = -0.46602 HELP ...
  10. Calculus

    Consider the function f(x)=sin(1/x) Find a sequence of x-values that approach 0 such that sin (1/x)=0 sin (1/x)=1 sin (1/x)=-1 Is sin sin (1/x)=0 and sin (1/x)=-1 does not exist. What is sin (1/x)=1 then.
  11. trig

    The expression 4 sin x cos x is equivalent to which of the following? (Note: sin (x+y) = sin x cos y + cos x sin y) F. 2 sin 2x G. 2 cos 2x H. 2 sin 4x J. 8 sin 2x K. 8 cos 2x Can someone please explain how to do this problem to me?
  12. Calculus 12th grade (double check my work please)

    1.)Find dy/dx when y= Ln (sinh 2x) my answer >> 2coth 2x. 2.)Find dy/dx when sinh 3y=cos 2x A.-2 sin 2x B.-2 sin 2x / sinh 3y C.-2/3tan (2x/3y) D.-2sin2x / 3 cosh 3yz...>> my answer. 2).Find the derivative of y=cos(x^2) with respect to x. A.-sin (2x) B.-2x sin (x^2...
  13. Calculus

    Consider the function f(x)=sin(1/x) Find a sequence of x-values that approach 0 such that (1) sin (1/x)=0 {Hint: Use the fact that sin(pi) = sin(2pi)=sin(3pi)=...=sin(npi)=0} (2) sin (1/x)=1 {Hint: Use the fact that sin(npi)/2)=1 if n= 1,5,9...} (3) sin (1/x)=-1 (4) Explain ...
  14. Calculus

    Consider the function f(x)=sin(1/x) Find a sequence of x-values that approach 0 such that (1) sin (1/x)=0 {Hint: Use the fact that sin(pi) = sin(2pi)=sin(3pi)=...=sin(npi)=0} (2) sin (1/x)=1 {Hint: Use the fact that sin(npi)/2)=1 if n= 1,5,9...} (3) sin (1/x)=-1 (4) Explain ...
  15. Trig

    Given: cos u = 3/5; 0 < u < pi/2 cos v = 5/13; 3pi/2 < v < 2pi Find: sin (v + u) cos (v - u) tan (v + u) First compute or list the cosine and sine of both u and v. Then use the combination rules sin (v + u) = sin u cos v + cos v sin u. cos (v - u) = cos u cos v + ...
  16. math

    find all solutions in the interval [0,2 pi) sin(x+(3.14/3) + sin(x- 3.14/3) =1 sin^4 x cos^2 x Since sin (a+b) = sina cosb + cosb sina and sin (a-b) = sina cosb - cosb sina, the first problem can be written 2 sin x cos (pi/3)= sin x The solution to sin x = 1 is x = pi/2 For ...
  17. math

    Prove that for all real values of a, b, t (theta): (a * cos t + b * sin t)^2 <= a^2 + b^2 I will be happy to critique your work. Start on the left, square it, (a * cos t + b * sin t)^2 = a^2 (1 - sin^2t) + 2ab sin t cost+ b^2 (1 - cos^2 t)= a^2 + b^2 - (a sin t - b cos t)^2...
  18. calculus

    Find complete length of curve r=a sin^3(theta/3). I have gone thus- (theta written as t) r^2= a^2 sin^6 t/3 and (dr/dt)^2=a^2 sin^4(t/3)cos^2(t/3) s=Int Sqrt[a^2 sin^6 t/3+a^2 sin^4(t/3)cos^2(t/3)]dt =a Int Sqrt[sin^4(t/3){(sin^2(t/3)+cos^2(t/3)}]dt=a Int Sqrt[sin^4(t/3)dt =a ...
  19. math

    Can you please check my work. A particle is moving with the given data. Find the position of the particle. a(t) = cos(t) + sin(t) s(0) = 2 v(0) = 6 a(t) = cos(t) + sin(t) v(t) = sin(t) - cos(t) + C s(t) = -cos(t) - sin(t) + Cx + D 6 = v(0) = sin(0) -cos(0) + C C=7 2= s(0) = -...
  20. Math

    Show that for real x that {[cos x + 2 sin x + 1]/[cos x + sin x] } cannot have a value between 1 and 2. Let y = [(cos x+2 sin x + 1)/(cos x + sin x) ] y(cos x + sin x) = (cos x + 2 sin x + 1) sin x(y-2) + cos x(y-1)=1 , I just feel that this isn't the way to do this.. Any ...
  21. Trigonometry

    I need help with I just can't seem to get anywhere. this is as far as I have got: Solve for b arcsin(b)+ 2arctan(b)=pi arcsin(b)=pi-2arctan(b) b=sin(pi-2arctan(b)) Sub in Sin difference identity let 2U=(2arctan(b)) sin(a-b)=sinacosb-cosasinb =(sin(pi))(cos(2U))-(cos(pi))(sin(...
  22. Calculus

    Hello, Could somebody kindly check my answer for the following question? Find the derivative of the following function: h(x)=3e^(sin(x+2)) h'(x)=3'(e^(sin(x+2))+3(e^(sin(x+2))' h'(x)=0(e^(sin(x+2))+3(e^(sin(x+2))(cos(1)) h'(x)=3cos1(e^(sin(x+2)) I would greatly appreciate your...
  23. Limit Calculas

    Evaluate lim->4 sin(2y)/tan(5y) Here is what I have so far. I am not sure the next steps. Can someone help me? 1. sin(2y)/(sin(5y)*cos(5y)) 2. (sin(2y)*cos(5y))/sin(5y)
  24. calculus

    Evaluate lim->4 sin(2y)/tan(5y) Here is what I have so far. I am not sure the next steps. Can someone help me? 1. sin(2y)/(sin(5y)*cos(5y)) 2. (sin(2y)*cos(5y))/sin(5y)
  25. pre calc trig check my work please

    sin x + cos x -------------- = ? sin x sin x cos x ----- + ----- = sin x sin x cos x/sin x = cot x this is what i got, the problem is we have a match the expression to the equation work sheet and this is not one of the answers. need to figure out what im doing wrong so i can ...
  26. Integral

    That's the same as the integral of sin^2 x dx. Use integration by parts. Let sin x = u and sin x dx = dv v = -cos x du = cos x dx The integral is u v - integral of v du = -sinx cosx + integral of cos^2 dx which can be rewritten integral of sin^2 x = -sinx cos x + integral of (...
  27. math

    Given that sin x + sin y = a and cos x + cos y =a, where a not equal to 0, express sin x + cos x in terms of a. attemp: sin x = a - sin y cos x = a - cos y sin x + cos x = 2A - (sin y + cos y)
  28. Precal

    I do not understand how to do this problem ((sin^3 A + cos^3 A)/(sin A + cos A) ) = 1 - sin A cos A note that all the trig terms are closed right after there A's example sin A cos A = sin (A) cos (A) I wrote it out like this 0 = - sin^6 A - cos^6 A + 2sin^3 A cos^3 A - 2sin^3 ...
  29. trig

    it says to verify the following identity, working only on one side: cotx+tanx=cscx*secx Work the left side. cot x + tan x = cos x/sin x + sin x/cos x = (cos^2 x +sin^2x)/(sin x cos x) = 1/(sin x cos x) = 1/sin x * 1/cos x You're almost there. thanks so much! i could not figure...
  30. Trig

    If angle A is 45 degrees and angle B is 60 degrees. Find sin(A)cos(B), find cos(A)sin(B), find sin(A)sin(B), and find cos(A)cos(B) The choises for the first are: A. 1/2[sin(105)+sin(345)] B. 1/2[sin(105)-sin(345)] C. 1/2[sin(345)+cos(105)] D. 1/2[sin(345)-cos(105)] You don't ...
  31. maths

    Prove: sin^212+sin^221+sin^239+sin^248=1+sin^29+sin^218
  32. trigonometry (please double check this)

    Solve the following trig equations. give all the positive values of the angle between 0 degrees and 360 degrees that will satisfy each. give any approximate value to the nearest minute only. 1. sin2Į = (sqrt 3)/2 2. sin^2Į = cos^2Į + 1/2 3. sin 2x - cosx = 0 4. cos 4x...
  33. d/dx

    d/dx( ln |sin(pi/x)| ) = ? Thanks. If those are absolute value signs, the derivative will not exist when sin (pi/x) = 0, because of the sign change that occurs there. Assume sin (pi/x) > 0 Let u(x) = pi/x and v(x) = sin x, and use the chain rule. d/dx ln v(u(x))= d/dv dv/du...
  34. math

    Proving Trigonometric Identities 1. sec^2x + csc^2x= (sec^2 x)(csc^2 x) 2. sin ^3 x / sin x - cos 3x / cos x = 2 3. 1- cos x/ sin x= sin x/ 1+ cos x 4. 2 sin x cos ^2 (x/2)- 1/x sin (2x) = sinx 5. cos 2 x + sin x/ 1- sin x= 1+ 2 sin x
  35. calculus

    Find the points on the curve y= (cos x)/(2 + sin x) at which the tangent is horizontal. I am not sure, but would I find the derivative first: y'= [(2 + sin x)(-sin x) - (cos x)(cos x)]/(2 + sin x)^2 But then I don't know what to do or if that is even correct??? Would I ...
  36. Calculus

    Evaluate the integral. S= integral sign I= absolute value S ((cos x)/(2 + sin x))dx Not sure if I'm doing this right: u= 2 + sin x du= 0 + cos x dx = S du/u = ln IuI + C = ln I 2 + sin x I + C = ln (2 + sin x) + C Another problem: S ((sin (ln x))/(x)) dx I don't even know what...
  37. Pre calc

    sin(θ − ϕ); tan(θ) = 5/12 θ in Quadrant III, sin(ϕ) = − sqaure root10/10 ϕ in Quadrant IV. I used the sin equation sin(a)cos(b)-sin(a)cos(b) However I am still getting the wrong answer
  38. Calculus

    Use a Riemann sum with n = 3 terms and the right endpoint rule to approx. ∫(1, 2) sin(1/x)dx. My teacher just needs the terms written out, no need to add or multiply. This is a problem she did up on the board, so here's her answer: sin(4/3)(1/3) + sin(5/3)(1/3) + sin(2)(...
  39. Trigonometry

    Prove the identity sin(x+y+z)+sin(x+y-z)+sin(x-y+z)+ sin(x-y-z) = 4 sin(x)cos(y)cos(z) This identity is so long and after i tried to expand the left side and it just looked something crap Thanks for you help :)
  40. trigonometry HELP pleasE!

    these must be written as a single trig expression, in the form sin ax or cos bx. a)2 sin 4x cos4x b)2 cos^2 3x-1 c)1-2 sin^2 4x I need to learn this!! if you can show me the steps and solve it so I can learn I'd be grateful!!! 1) apply the formula for sin 2z 2)3) cos^2z + sin^...
  41. Calculus

    Consider the function f(x)=sin(1/x) Find a sequence of x-values that approach 0 such that sin (1/x)=0 sin (1/x)=1 sin (1/x)=-1 Is sin sin (1/x)=0 and sin (1/x)=-1 does not exist. What is sin (1/x)=1 then. How would I show the sequence of values, any help would be greatly ...
  42. MathsSs triG

    Consider sin(x-360)sin(90-x)tan(-x)/cos(90+x) 1.A.SIMPLIFY sin(x-360)sin(90-x)tan(-x)/cos(90+x) to a single trigonometric ratio B.hence or otherwise without using a calculator,solve for X if 0<X<360. sin(x-360)sin(90-x)tan(-x)/cos(90+x) =0,5 2.A.prove that 8/sin^2A - 4/1...
  43. Public High School Pre Calculus HH

    Ok I do not know how to do this problem. I know that csc is simply sin^-1 sin (- pi/12) csc ( (37 pi)/12 ok now I know this also sin (- pi /12 ) = - sin ( pi/12) not really sure how that helps I don't know were to go from here ( - sin (pi/12) )/(sin ( (25 pi)/12 ) )
  44. Trigonometry

    Does anyone have a good website that shows the proofs for these equations? sin(u+v) = sin(u)cos(v) + sin(v)cos(u) cos(u+v) = cos(u)cos(v) + sin(v)sin(u) Thanks!
  45. Trigonometry

    Please review and tell me if i did something wrong. Find the following functions correct to five decimal places: a. sin 22degrees 43' b. cos 44degrees 56' c. sin 49degrees 17' d. tan 11degrees 37' e. sin 79degrees 23'30' f. cot 19degrees 0' 25'' g. tan 64degrees 6' 45'' h. cos...
  46. Trig

    sin^4t-cos^4t/sin^2t cos^2t= sec^2t-csc^2t i have =(sin^2t+cos^2t)(sin^2t+cos^2t)/sin^2tcos^2t then do i go =(sin^2t+cos^2t)/sin^2tcos^2t stumped
  47. calculus/Trig

    Suppose you wish to express sin(3t) in terms of sint and cost. Apply the sum formula to sin(3t) = sin(t+2t) to obtain an expression that contains sin(2t)=sin(t+t) and cos(2t)=cos(t+t). Apply the sum formulas to those two expressions. Enter the resulting expression for sin(3t) ...
  48. Math Help

    Hi! Can someone help check this for me and see if I'm doing it right? Thanks!! :) Directions: Use the Half-Angle formulas to determine the exact value of sin(pi/12). Here's what I have: π/12 = ( 180° ) / 12 = 15°. = sin ( π/12 ) = sin 15° = sin ( 45° - 30°) = ...
  49. verifying trigonometric identities

    How do I do these problems? Verify the identity. a= alpha, b=beta, t= theta 1. (1 + sin a) (1 - sin a)= cos^2a 2. cos^2b - sin^2b = 2cos^2b - 1 3. sin^2a - sin^4a = cos^2a - cos^4a 4. (csc^2 t / cot t) = csc t sec t 5. (cot^2 t / csc t) = csc t = sin t
  50. Trig.

    tan^2BeatacscBeta-tan^2 (simplify) (sin/cos)^2Beta times 1/sin-(sin/cos)^2 (sin^2/cos^2)-(sin^2/cos^2)=-sin/cos Is this correct?
  51. Geometry One multiple choice question!

    Write the ratios for sin A and cos A. {picture is of a right triangle, ABC. segment AC is 8, segment AB is 17, and segment CB is 15.} sin A=15/17, cos A=8/17 sin A=15/8, cos A=8/17 sin A=15/17, cos A=8/15 sin A=8/17, cos A=15/17
  52. Geometry Please Help With One Multiple Choice

    Write the ratios for sin A and cos A. {picture is of a right triangle, ABC. segment AC is 8, segment AB is 17, and segment CB is 15.} sin A=15/17, cos A=8/17 sin A=15/8, cos A=8/17 sin A=15/17, cos A=8/15 sin A=8/17, cos A=15/17
  53. math

    how would you prove that sin^2(a)-cos^2(b)= sin^2(b)-cos^2(a). i'm not completely sure that this is right but i used the difference of two squares on it to get (sin(a)+cos(b))(sin(a)-cos(b)) then after that i am stuck. please help
  54. Math, Pre-Calc

    the original problem was: Solve: sin(3x)-sin(x)=cos(2x) so far i've gooten to: sin(x)(2sin(x)cos(x)-1)=cos^2(x)-sin^2(x) Where would I go from here?
  55. Math(Please help)

    2) Use the sum and difference identites sin[x + pi/4] + sin[x-pi/4] = -1 sinx cospi/4 + cosxsin pi/4 + sinx cos pi/4 - cosx sin pi/4 = -1 2 sin x cos pi/4 =-1 cos pi/4 = sqr2/2 2sin^x(sqrt2/2) = -1 sin x = -sqrt2 x = 7pi/4 and 5pi/4 Am I correct?
  56. Precalc

    Let x, y, and z be real numbers such that cos(x) + cos(y) + cos(z) = sin(x) + sin(y) + sin(z) = 0. Prove that cos(2x) + cos(2y) + cos(2z) = sin(2x) + sin(2y) + sin(2z) = 0.
  57. Math Help Please

    What are the ratios for sin A and cos A? The diagram is not drawn to scale. Triangle Description- AB = 29 AC = 20 BC - 21 A. sin A = 20/29, cos A = 21/29 B. sin A = 21/29, cos A = 20/21 C. sin A = 21/29, cos A = 20/29****? D. sin A = 21/20, cos A = 20/21 Please help and explain!
  58. maths

    Choose the option that gives an expression for the indefinite integral ʃ (cos(4x) + 2x^2)(sin(4x) − x) dx. In each option, c is an arbitrary constant. Options A cos(4x) + 2x^2 +c B -1/8cos(4x) + 2x^2)^2 +c C 1/4 (sin(4x) − x)^2 + c D (1/(2 (sin(4x) − x...
  59. maths

    Choose the two options which are true for all values of x 1) cos (x) = cos ( x – pie/2) 2) sin (x + pie/2) = cos (x – pie/2) 3) cos (x) = sin (x – pie/2) 4) sin (x) = sin (x + 4pie) 5) sin (x) = cos (x – pie/2) 6) sin^2 (x) + cos^2 (x) = pie would it be 1 and 3 ?? I ...
  60. antiderivatives

    i need the antiderivative of sinxcosx dx for intergral pie/2 to 0 thanks. sin(x)cos(x)dx = sin(x)d[sin(x)] = 1/2d[sin^2(x)]
  61. pre-cal

    Simplify the given expression........? (2sin2x)(cos6x) sin 2x and cos 6x can be expressed as a series of terms that involve sin x or cos x only, but the end result is not a simplification. sin 2x = 2 sinx cosx cos 6x = 32 cos^6 x -48 cos^4 x + 18 cos^2 x - 1 I assume you are ...
  62. Math

    the original problem was: Solve: sin(3x)-sin(x)=cos(2x) so far i've gotten to: sin(x)(2sin(x)cos(x)-1)=cos^2(x)-sin^2(x) Where would I go from here?
  63. Math

    the original problem was: (sin x + cos x)^2 + (sin x - cos x)^2 = 2 steps too please I got 1 for (sin x + cos x)^2 but then what does (sin x - cos x)^2 become since it's minus?
  64. Trig!

    The identities cos(a-b)=cos(a)cos(b)sin(a)sin(b) and sin(a-b)=sin(a)cos(b)-cos(a)sin(b) are occasionally useful. Justify them. One method is to use rotation matricies. Another method is to use the established identities for cos(a+b) and sin (a+b).
  65. math

    Determine all the possible values of x where 0 deg is more than or equal to x and x is more or equal to 360 deg such that i'm not sure the solution, please correct it, sin x sec x - 3 sin x = 0 the solution: sin x 1/cos x - 3 sin x = 0 sin x - 3 sin x = cos x then i don't know...
  66. Math

    Helle, i need help for simplify the expression: [( cos x) ( sin x) - ( sin x) ( - sin x)] / ( sin x) ²
  67. Adv function

    sin(7x)= sin(x)[cos^2(3x)-sin^2(3x)]+2cos(x)cos(3x)sin(3x) I tried for an hour but still don't know how. Plzz help
  68. Math

    State the restrictions on the variables for these trigonometric identities. a)(1 + 2 sin x cos x)/ (sin x + cos x) = sin x + cos x b) sin x /(1+ cos x) = csc x - cot x
  69. Math (Linear Systems)

    28 N + T2 sin 12 = T1 sin 42 T2 cos 12 = T1 cos 42 T2 sin 12 + T3 sin 54 = W2 T2 cos 12 = T3 cos 54 Im solving for T1,2,3 and W2 I just cant seem to get the system to work
  70. Calculus I

    Find the derivative of f(x) = sin^2 (e^sin^2 x) I wonder if I'm right F'(x) = 2cos(e^sin^2 x) (sin^2 x e^sin^2 x -1)
  71. precalc

    prove the identity: cos^4 - sin^4 = cos^2 - sin^2 (cos^2 + sin^2)(cos^2 - sin^2) cos^2 + sin^2 = 1 cos^2 - sin^2 = cos^2 - sin^2 is this correct?
  72. Math(Please help)

    1)tan Q = -3/4 Find cosQ -3^2 + 4^2 = x^2 9+16 = sqrt 25 = 5 cos = ad/hy = -4/5 Am I correct? 2) Use the sum and difference identites sin[x + pi/4] + sin[x-pi/4] = -1 sinx cospi/4 + cosxsin pi/4 + sinx cos pi/4 - cosx sin pi/4 = -1 2 sin x cos pi/4 =-1 cos pi/4 = sqr2/2 2sin^x...
  73. Math

    I need help solving for all solutions for this problem: cos 2x+ sin x= 0 I substituted cos 2x for cos^2x-sin^2x So it became cos^2(x)-sin^2(x) +sinx=0 Then i did 1-sin^2(x)-sin^2(x)+sinx=0 = 1-2sin^2(x)+sinx=0 = sinx(-2sinx+1)=-1 What did i do wrong?? the real solutions are ...
  74. MATH

    1.)Find the exact solution algebriacally, if possible: (PLEASE SHOW ALL STEPS) sin 2x - sin x = 0 2.) GIVEN: sin u = 3/5, 0 < u < ï/2 Find the exact values of: sin 2u, cos 2u and tan 2u using the double-angle formulas. 3.)Use the half-angle formulas to determine the ...
  75. COLLEGE CALCULUS. HELP!

    i don't know how to start this problem. i don't like cos and sin. im so confuse. 1.f(x)=sin(sin(x)), find f'(x) 2.f(x)= 4sin^4x, find f'(x). this problem i couldn't find it in my math book. i never see it before. because of sin exponent 4 -->sin^4
  76. Trig

    Solve in terms of sine and cosine: sec(x) csc(x)- sec(x) sin(x) so far I have: 1/cos(x) 1/sin(x) - 1/cos(x) sin(x) I am not sure where to go to from there. The book says the answer is cot(x) or cos(x)/sin(x) Thank you in advance.
  77. Integration by Parts

    integral from 0 to 2pi of isin(t)e^(it)dt. I know my answer should be -pi. **I pull i out because it is a constant. My work: let u=e^(it) du=ie^(it)dt dv=sin(t) v=-cos(t) i integral sin(t)e^(it)dt= -e^(it)cos(t)+i*integral cost(t)e^(it)dt do integration by parts again, then I ...
  78. Math

    Solve this equation algebraically: (1-sin x)/cos x = cos x/(1+sin x) --- I know the answer is an identity, and when graphed, it looks like cot x. I just don't know how to get there. I tried multiplying each side by its conjugate, but I still feel stuck. This is what I have so ...
  79. precalculus

    For each of the following determine whether or not it is an identity and prove your result. a. cos(x)sec(x)-sin^2(x)=cos^2(x) b. tan(x+(pi/4))= (tan(x)+1)/(1-tan(x)) c. (cos(x+y))/(cos(x-y))= (1-tan(x)tan(y))/(1+tan(x)tan(y)) d. (tan(x)+sin(x))/(1+cos(x))=tan(x) e. (sin(x-y...
  80. math

    I'm trying to find the convolution f*g where f(t)=g(t)=sin(t). I set up the integral and proceed to do integration by parts twice, but it keeps working out to 0=0 or sin(t)=sin(t). How am I supposed to approach it? integral (sin(u)sin(t-u)) du from 0 to t.
  81. Trig

    Sin(X-y)sin(x+y)=sin^2 x - sin^2 y work on one side only...so i worked on the right =(sinx-siny)(sinx+siny) does that equal sin(x-y)sin(x+y)??? help!
  82. trig!!

    Sin(X-y)sin(x+y)=sin^2 x - sin^2 y work on one side only...so i worked on the right =(sinx-siny)(sinx+siny) does that equal sin(x-y)sin(x+y)??? help!
  83. Math

    Evaluate *Note - We have to find the exact value of these. That I know to do. For example sin5π/12 will be broken into sin (π/6) + (π/4) So... sin 5π/12 sin (π/6) + (π/4) sin π/6 cos π/4 + cos π/6 sin π/4 I get all those steps...
  84. math

    Create sketches by hand of the following sine functions, showing at least one full period and state the domain and range. Submit them to your teacher using the drop box above. It may be easiest for you to scan your hand drawn sketches and submit the scan file. Part A: ...
  85. Precalc

    1. Prove sin - cos +1/ sin + cos - 1 = sin +1/cos 2. 1+ sin/ 1- sin = (sec + tan)^2 Thanks!!
  86. Derivatives

    what is derivative of sin^2 (3x-1)^2 ? dy/dx (sin^2 (x))= 2 sin x cos x dy/dx (3x-1)^2= 6(3x-1) chain rule? = 2 sin ((3x-1)^2) cos ((3x-1)^2) * 6(3x-1) Please help. Thank you
  87. calculus

    Could someone check my reasoning? thanx Find the derivative of the function. sin(sin[sinx]) I need to use the chain rule to solve. So I take the derivative sin(sin[sinx) first. Then multiply that by the inside which is the derivative of sin[sinx]. And multiply that by ...
  88. Mathematics-Integration

    Question: For any positive integer n,show that integrate.[(sin x)^2n dx ] from o - π/2 = [(2n)!*π]/[(2)^(2n+1)*(n!)^2 ] What I thought: Let I =int.[(sinx)^2n dx] And again I= int.[ (sin(π/2-x))^2n dx] = int.[ (cos)^2n dx] 2I= int.[(sin x)^2n + (cos x)^2n dx] 2I= int.[ (sin ...
  89. Trigonometry

    Hello all, In our math class, we are practicing the trigonometric identities (i.e., sin^2(x)+cos^2(x)=1 or cot(x)=cos(x)/sin(x). Now, we are working on proofs that two sides of an equation are equal (for example, sin(x)*csc(x)=1; sin(x)csc(x)=sin(x)/sin(x)=1; 1=1). I am not ...
  90. trigonometry

    find without tables or calculator. (1) sin^2 (22 1/2)- cos^2 (22 1/2) (2) sin 60 cos 30 + sin 30 cos 60 (3) cos(90-y) = sin 56degree 47^i
  91. Maths

    Cos^4(θ)/cos^2(α) + sin^4(θ)/ sin^2(α)=1 Prove that cos^4 alpha/cos^ thetha + sin^4alpha/ sin^2thetha= 1
  92. Math - Calculus

    The identity below is significant because it relates 3 different kinds of products: a cross product and a dot product of 2 vectors on the left side, and the product of 2 real numbers on the right side. Prove the identity below. | a × b |² + (a • b)² = |a|²|b|² My work, ...
  93. Pre-Calc

    How do I solve this? My work has led me to a dead end. tan(45-x) + cot(45-x) =4 my work: (tan45 - tanx)/(1+ tan45tanx) + (cot45 - cotx)/(1 + cot45cotx) = 4 (1-tanx)/(1+tanx) + (1-cotx)/(1+cotx) = 4 Then I found a common denominator, giving me this: (2-2cotxtanx)/(1+cotx+tanx+...
  94. Trig

    4. Asked to simplify the expression sin(180−è), Rory volunteered the following solution: sin(180−è) = sin 180−sin è, and, because sin 180 is zero, it follows that sin(180−è) is the same as −sin è. Is this answer correct? If not, what is a ...
  95. Math

    Which of the following expressions is equivalent to (cos(3x))/sin(x)cos(x))? csc(x) cos(2x) - sec(x) sin(2x) sec(x) cos(2x) - csc(x) sin(2x) sec(x) cos(x) - csc(x) sin(x) csc(x) cos(x) - sec(x) sin(x) This is my last question and I've tried solving it repeatedly but now I ...
  96. Pre-Calculus

    I don't understand,please be clear! Prove that each equation is an identity. I tried to do the problems, but I am stuck. 1. cos^4 t-sin^4 t=1-2sin^2 t 2. 1/cos s= csc^2 s - csc s cot s 3. (cos x/ sec x -1)- (cos x/ tan^2x)=cot^2 x 4. sin^3 z cos^2 z= sin^3 z - sin^5 z
  97. Math

    Asked to simplify the expression sin(180−è), Rory volunteered the following solution: sin(180−è) = sin 180−sin è, and, because sin 180 is zero, it follows that sin(180−è) is the same as...
  98. Calculus

    Integrate 1/sinx dx using the identity sinx=2(sin(x/2)cos(x/2)). I rewrote the integral to 1/2 ∫ 1/(sin(x/2)cos(x/2))dx, but I don't know how to continue. Thanks for the help. Calculus - Steve, Tuesday, January 12, 2016 at 12:45am 1/2 ∫ 1/(sin(x/2)cos(x/2))dx let u...
  99. calculus

    using the squeeze theorem, find the limit as x->0 of x*e^[8sin(1/x)] what i did was: -1<=sin(1/x)<=1 -8<=8*sin(1/x)<=8 e^(-8)<=e^[8*sin(1/x)]<=e^(8) x*e^(-8)<=x*e^[8*sin(1/x)]<=x*e^(8) lim x->0 [x*e^(-8)] = 0 lim x->0 [x*e^(8)] = 0 hence, lim x...
  100. calculus

    Evaluate the integral of (x)cos(3x)dx A. (1/6)(x^2)(sin)(3x)+C B. (1/3)(x)(sin)(3x)-(1/3)(sin)(3x)+C C. (1/3)(x)(sin)(3x)+(1/9)(cos)(3x)+C D. (1/2)(x^2)+(1/18)(sin)^2(3x)+C
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