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Let z be a complex number such that z = 2(cos 8∘ + i cos 82∘).Then z^5 can be expressed as r(sin α∘+ i cos α∘), where r is a real number and 0 ≤ α ≤ 90. What is

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  1. Math (Trigonometry [Polar Form])

    Let z be a complex number such that z = 2(cos 8∘ + i cos 82∘).Then z^5 can be expressed as r(sin α∘+ i cos α∘), where r is a real number and 0 ≤ α ≤ 90. What is the value of r+α? Hint to solve: Example Question: Let z be a complex number
  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 +
  3. 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 -
  4. math

    Determine exact value of cos(cos^-1(19 pi)). is this the cos (a+b)= cos a cos b- sina sin b? or is it something different. When plugging it in the calculator, do we enter it with cos and then the (cos^-1(19 pi)).
  5. math

    Find the exact value of cos 300 degrees. thanks guys cos 300 = 1/2 = 0.500 how do you know? I am supposed to show my work. You ought to know the rule on 30-60-90 triangles. If the hyp is 2, the shorter side is 1, and the longer side is sqrt3. what does
  6. Precalculus

    Solve Cos^2(x)+cos(x)=cos(2x). Give exact answers within the interval [0,2π) Ive got the equation down to -cos^2(x)+cos(x)+1=0 or and it can be simplified too sin^2(x)+cos(x)=0 If you could tell me where to go from either of these two, it would be great
  7. maths

    Find the roots of z^6 + 1 and hence resolve z^6 + 1into read quadratic factors; deduce that cos3x = 4[cos(x) -cos(pi/6)][(cos(x) -cos(pi/2)][(cos(x) -cos(5pi/6)]
  8. maths

    Find the roots of z^6 + 1 and hence resolve z^6 + 1into read quadratic factors; deduce that cos3x = 4[cos(x) -cos(pi/6)][(cos(x) -cos(pi/2)][(cos(x) -cos(5pi/6)]
  9. Calc.

    Differentiate. y= (cos x)^x u= cos x du= -sin x dx ln y = ln(cos x)^x ln y = x ln(cos x) (dy/dx)/(y)= ln(cos x) (dy/dx)= y ln(cos x) = (cos x)^x * (ln cos x) (dx/du)= x(cos x)^(x-1) * (-sin x) = - x sin(x)cos^(x-1)(x) (dy/dx)-(dx/du)=
  10. calculus

    Differentiate. y= (cos x)^x u= cos x du= -sin x dx ln y = ln(cos x)^x ln y = x ln(cos x) (dy/dx)/(y)= ln(cos x) (dy/dx)= y ln(cos x) = (cos x)^x * (ln cos x) (dx/du)= x(cos x)^(x-1) * (-sin x) = - x sin(x)cos^(x-1)(x) (dy/dx)-(dx/du)=
  11. Math - Solving Trig Equations

    What am I doing wrong? Equation: sin2x = 2cos2x Answers: 90 and 270 .... My Work: 2sin(x)cos(x) = 2cos(2x) sin(x) cos(x) = cos(2x) sin(x) cos(x) = 2cos^2(x) - 1 cos(x) (+/-)\sqrt{1 - cos^2(x)} = 2cos^2(x) - 1 cos^2(x)(1 - cos^2(x)) = 4cos^4(x) - 4cos^2(x)
  12. Calculus

    Determine the polar form of the complex number 3 - 2i. Express the angle theta in degrees, where 0
  13. Trigonometry

    There is an arbitrary triangle with angles A, B, and C and sides of lengths a, b, and c. Angle A is opposite side a. How do I get the formulas: b * cos C + c * cos B = a c * cos A + a * cos C = b a * cos B + b * cos A = c Are these standard trig formulas?
  14. Trigonometry

    Express each of the following in terms of the cosine of another angle between 0 degrees and 180 degrees: a) cos 20 degrees b) cos 85 degrees c) cos 32 degrees d) cos 95 degrees e) cos 147 degrees f) cos 106 degrees My answer: a) - cos 160 degrees b) - cos
  15. 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
  16. Mathematics - Trigonometric Identities - Reiny

    Mathematics - Trigonometric Identities - Reiny, Friday, November 9, 2007 at 10:30pm (sinx - 1 -cos^2x) (sinx + 1 - cos^2x) should have been (sinx - 1 + cos^2x) (sinx + 1 - cos^2x) and then the next line should be sin^2x + sinx - cos^2xsinx - sinx - 1 +
  17. calculus

    pleaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaasw help can you pleaaaaase help me find the area between y=cos(4x) and y=1-cos(4x) 0
  18. Trigonometry

    Write each expression in the standard form for a complex number, a + bi. A. [3(cos(27°)) + isin(27°)]^5 B. [2(cos(40°)) + isin(40°)]^6 For A i got 2.67+1.36i and for B i got 1.53+1.29i
  19. Trigonometry Help please

    Write each expression in the standard form for a complex number, a + bi. A. [3(cos(27°)) + isin(27°)]^5 B. [2(cos(40°)) + isin(40°)]^6 For A i got 2.67+1.36i and for B i got 1.53+1.29i
  20. Trigonometry

    Write equivalent equations in the form of inverse functions for a.)x=y+cos è b.)cosy=x^2 (can you show how you would solve) a.) x= y+ cos è cos è = x-y theta = cos^-1(x-y) b.) cosy=x^2 cos(y) = x^2 y = Cos^-1(x^2)
  21. Trig. Law of Cosines

    Show that any triangle with standard labeling... a^2+b^2+c^2/2abc = cos(alpha)/a + cos(beta)/b + cos(gamma)/c I don't get it. Can someone please help me. Start here with the law of cosines: a^2 = b^2 + c^2 -2bc Cos A b^2 = a^2 + c^2 -2ac Cos B c^2 = a^2 +
  22. 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:
  23. 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
  24. self-study calculus

    Sketch the curve with the given vector equation. Indicate with an arrow the direction in which t increases. r(t)=cos(t)I -cos(t)j+sin(t)k I don't know what to do. I let x=cos(t), y=-cos(t) and z= sin(t). Should I let t be any number and get the equal
  25. 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 +
  26. Calculus II

    What is sin(i) -- (sin of the imaginary number, i) What is cos(i)-- cosine of the imaginary number, i orrr tan(1+i) You can derive these things from the equation: Exp(i x) = cos(x) + i sin(x) ---> sin(x) = [Exp(ix) - Exp(-ix)]/(2i) cos(x) = [Exp(ix) +
  27. Maths

    use the formula cos(x+iy)=cosxcosiy-sinxsiniy to find two imaginary numbers whose cosine is 3 cos(x+iy)=cosxcosiy-sinxsiniy = cos(x)cosh(y) - i sin(x)sinh(y) = 3 Equating imaginary parts gives: sin(x)sinh(y) = 0 You know that y cannot be zero, otherwise
  28. Maths

    How do I do this Need details solution to follow up prove that cos(a)+cos(a+b)+cos(a+2b)+....+cos(a+(n-1)b)={cos(a+((n-1)/2)bsin(nB/2)}/½sinb for all N£N
  29. Algebra

    Write an equation for the translation of the function. y = cos x; translated 6 units up A. y = cos x- ­ 6 B. y = cos(x + 6) C. y = cos x + 6 D. y = cos(x ­ 6) I think its B or c..
  30. Maths:Trigonometry

    How do I do this Need details solution to follow up prove that cos(a)+cos(a+b)+cos(a+2b)+....+cos(a+(n-1)b)={cos(a+((n-1)/2)bsin(nB/2)}/½sinb for all N£N ???
  31. Pre-Cal (Trig) Help?

    The following relationship is known to be true for two angles A and B: cos(A)cos(B)-sin(A)sin(B)=0.957269 Express A in terms of the angle B. Work in degrees and report numeric values accurate to 2 decimal places. So I'm pretty lost on how to even begin
  32. trig

    Show that 1-cos2A/Cos^2*A = tan^2*A 1-cos2A/Cos^2*A = [Cos^2(A) - Cos(2A)]/Cos^2(A). Substitute: Cos(2A) = 2Cos^2(A) - 1: [1 - Cos^2(A)]/Cos^2(A)= Sin^2(A)/Cos^2(A) = tan^2(A)
  33. Trig Help!

    Question: Trying to find cos π/12, if cos π/6 = square root 3 over 2, how to find cos π/12 using DOUBLE angle formula? This is what I got so far.. cos 2(π/6) = cos (π/6 + π/6) = (cos π/6)(cos π/6) - (sin π/6)(sin π/6) = cos^2 π/6 - sin^2 π/6 Is
  34. math

    if cos(B-C)+cos(C-A)+cos(A-B)=-3/2 then prove that cosA+cosB+cosC=O and sinA+sinB+sinC=O after that prove that cos(B-C)=cos(C-A)=cos(A-B)=-1/2
  35. 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 +
  36. MATH

    Hi, I really need help with these questions. I did some of them halfway, but then I got stuck. Would you please help me? Thank you so much. Prove the identity.... 1. sec x + tan x(1-sin x/cos x)=1 1/cos x + sin x/cos x(cos^2 x/cos x)=1 1+sin x/cos
  37. math

    Express the following in simplest form: (complex fraction) Sin(x) - Cos(x) Cos(x) Sin(x) _______________ 1 - 1 Cos(x) Sin(x)
  38. Studying for Pre Cal exam

    Find the fourth roots of − 1/2 + (square root)3/2 i Write the roots in trigonometric form. A - w 1=cos(35°)+isin(35°) w2 =cos(125°)+isin(125°) w3 =cos(215°)+isin(215°) w4 =cos(305°)+isin(305°) B - w1 =cos(40°)+isin(40°) w2
  39. Math - Solving Trig Equations

    Solve each equation for o is less than and/or equal to theta is less than and/or equal to 360 -- sin^2x = 1 = cos^2x -- Work: cos^2x - cos^2x = 0 0 = 0 -- Textbook Answers: 90 and 270 -- Btw, how would you isolate for cos^2x = 0? Would it be... x = cos^-1
  40. calculus

    The limit represents the derivative of some function f at some number a. Select an appropriate f(x) and a. lim (cos(pi+h)+1)/h h->0 answers are f(x) = tan(x), a = pi f(x) = cos(x), a = pi/4 f(x) = cos(x), a = pi f(x) = sin(x), a = pi
  41. Math - Solving for Trig Equations

    Solve the following equation for 0 less than and/or equal to "x" less than and/or equal to 360 -- cos^2x - 1 = sin^2x -- Attempt: cos^2x - 1 - sin^2x = 0 cos^2x - 1 - (1 - cos^2x) = 0 cos^2x - 1 - 1 + cos^2x = 0 2cos^2x - 2 = 0 (2cos^2x/2)= (-2/2) cos^2x =
  42. Math

    Explain how to do this with steps please. 1. Simplify cos(x-y)+cos(x+y)/cosx I did some of these so far, don't know if it is correct. Formula: cosxcosy= cos(x+y)+cos(x-y)/2 cos(x-y)+cos(x+y)/cosx =cosxcosy/2cosx
  43. 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.
  44. Math, derivatives

    Let g(x) = sin (cos x^3) Find g ' (x): The choices are a) -3x^2sinx^3cos(cos x^3) b) -3x^2sinx^3sin(cos x^3) c) -3x^2cosx^3sin(cos x^3) d) 3x^2sin^2(cos x^3) I'm not exactly sure where I should start. Should I begin with d/dx of sin? Or do the inside
  45. Calculus - MathMate Please help

    ok, i tried to do what you told me but i cant solve it for c because they cancel each others out! the integral for the first one i got is [sin(c)cos(x)-cos(c)sin(x)+sin(x)+c] and the integral for the 2nd one i got is [-sin(c)cos(x)+cos(c)sin(x)-sin(x)+c] I
  46. Calculus

    which of the following integrals results from making the substitution u=x^3 in orer to find (squiggly vertical line)x^2cos(x^3)dx ~cos u du ~u^2 cos u du ~u^(2/3) cos u du1/3 os u du ~3 cos u du
  47. Math(Please check)

    Use the fundamental identities to simplify the expression. tan^2 Q / sec^2 Q sin^2/cos^2 / 1/cos^2 = sin^2 / cos^2 times cos^2 / 1 = The cos^2 cancels out so sin^2 is left. Is this correct?
  48. trigonomentry out of ideal help ah!crying

    compute.. Cos(1degree)+cos(3degree)+cos(5degree)+...+Cos(179degree) plz show working even an hint can,t help me.Have been do maths alday my brain is fried..Ah thanks
  49. calc.- trig substitution

    s- integral s 1/ [ (x^4) sq.rt(x^2+9)] i know x=3tanx sq.rt(x^2+9)= 3 secx dx= 3/[cos^2(x)] so far i know: = 1/ (3tan^4(x)) 3secx cos^2(x)) dx =1/ 81 [ (sin^4 (x)/cos^4 (x)) (1/cosx) (cos^2(x))] then i'm not really sure what to do next
  50. 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
  51. Trigonometry - LONESTAR

    Simplifying steps without using the calculator for: tan(cos^-1(-1/10)) cos(sin^−1(1/x)) Assume x is positive tan(cos^−1(12/13)) cos^−1(cos 150°) This is pretty much the entire section we are doing. My teacher is a robot and has us self teach
  52. trig

    2sin(x)cos(x)+cos(x)=0 I'm looking for exact value solutions in [0, 3π] So I need to find general solutions to solve the equation. But do I eliminate cos(x), like this... 2sin(x)cos(x)+cos(x)=0 2sin(x)cos(x)= -cos(x) 2sin(x) = -1 sin(x) = -1/2 at 4pi/3
  53. Math

    use Demoivre's Theorem to find the indicated power of the complex number. Express the result in standard form. (2+2i)^6 a=2 b=2 n=6 r=sqrt 2^2 + 2^2 = sqrt8 Q=7pi/4 (sqrt8)^6 = 512 512(cos 6/1 x 7pi/4) + i sin 6 x 7pi/4 512 (cos 21pi/2) + i sin (21pi/2)
  54. Math

    use Demoivre's Theorem to find the indicated power of the complex number. Express the result in standard form. (2+2i)^6 a=2 b=2 n=6 r=sqrt 2^2 + 2^2 = sqrt8 Q=7pi/4 (sqrt8)^6 = 512 512(cos 6/1 x 7pi/4) + i sin 6 x 7pi/4 512 (cos 21pi/2) + i sin (21pi/2)
  55. 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
  56. Trigonometry (repost Reiny)

    at 1:35am I posted ; Write equivalent equations in the form of inverse functions for a.)x=y+cos theta b.)cosy=x^2 my answers were a.) x= y+ cos theta cos theta = x-y theta = cos^-1(x-y) b.) cosy=x^2 cos(y) = x^2 y = Cos^-1(x^2) your post confused me a
  57. precalculus

    I don't understand this problem: (Tanө + cos ө)/ (sec ө + cot ө) so I start off like this: ={(sinө / cos ө)+cosө}{cos ө + (sinө/cosө)} =[(sin ө +cos^2ө) (cos^2ө +sin ө)]/ cos ө but what comes next?
  58. Trig/Precalc

    So I have two questions that have been puzzling me for quite some time and would really appreciate any help with either of them! (a) There are four positive intergers a, b, c, and d such that 4cos(x)cos(2x)cos(4x)=cos(ax)+cos(bx)+cos(cx)+cos(dx) for all
  59. Math

    Explain how to do this with steps please. 1. Simplify cos(x-y)+cos(x+y)/cosx Formula: cosxcosy= cos(x+y)+cos(x-y)/2 cos(x-y)+cos(x+y)/cosx =cosxcosy/2cosx
  60. Math

    Find the exact value of cos 1 degree + cos 2 degrees + cos 3 degrees + ... + cos 357 + cos 358 degrees + cos 359 degrees.
  61. Trigonometry(please Clarify)

    I posted before ; Write equivalent equations in the form of inverse functions for a.)x=y+cos theta b.)cosy=x^2 my answers were a.) x= y+ cos theta cos theta = x-y theta = cos^-1(x-y) b.) cosy=x^2 cos(y) = x^2 y = Cos^-1(x^2) your post confused me a little.
  62. trig

    how would you verify this trig identity (1+cos(x) / 1-cos(x)) - (1-cos(x) / 1+cos(x)) = 4cot(x)csc(x) ? help please!
  63. math

    Prove that for all real values of a, b, t (theta): (a * cos t + b * sin t)^2
  64. Math

    Prove each identity: a) 1-cos^2x=tan^2xcos^2x b) cos^2x + 2sin^2x-1 = sin^2x I also tried a question on my own: tan^2x = (1 – cos^2x)/cos^2x R.S.= sin^2x/cos^2x I know that the Pythagorean for that is sin^2x + cos^2x That's all I could do.
  65. Math

    Write the expression in terms of costheta and then simplify. cos^4theta - sin^4theta + sin^2theta Ans: cos^4 θ - 1 - cos^4 θ + 1 - cos^2 θ = -cos^2 θ
  66. Math

    Eliminate the parameter and write the corresponding rectangular equation whose graph represents the curve. x = sec Q y = cos Q x^2 + y^2 = 1/cos^2 + sin^2/cos^2 = x^2(1 +sin^2) = x^2(2-cos^2) x^2(2-1/x^2) = 2x^2 - 1 x^2 - y^2 = 1 My teacher said to use
  67. Calculus AP

    Use the table of integrals to find int cos^4 3x dx I found the table: ∫cos^n u du = (1/n)cos^(n-1)u sinu + (n-1/n)∫sin^(n-2)u du = 1/4 cos^(4-1)u sinu + (4-1/4)∫sin^(4-2) u du so what i did the problem: let u=3x then du=3dx =1/4*1/3 cos^3u sinu +
  68. Calculus

    Evaluate (Integral) sin 4x cos^2 4x dx. A. Cos^3(4x)/3 + C B. -Cos^3(4x)/3 + C C. Cos^3(4x)/12 + C D. -Cos^3(4x)/12 + C
  69. Calculus

    Find F '(x) for F(x) = integral[x^3 to 1](cos(t^4)dt) a. cos(x^7) b. -cos(x^12) c. -3x^2cos(x^12) d. cos(1) - cos(x^12)
  70. Calculus

    what is the limit n to infinite of cos1*cos(1/2)*cos(1/4)*cos(1/8)*cos(1/16)*...*cos(1/2^n)
  71. Calculus

    Evaluate the integral sin4x cos^2 4x dx A. cos^3 4x/3 +C B. - cos^3 4x/3 +C C. cos^3 4x/12 +C D. -cos^3 4x/12 +C
  72. 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
  73. math

    The complex number [2[cos(π/10)+isin(π/10)]]^5 can be written as a+bi. What is the value of a+b?
  74. Math

    Can someone please check my answers! 2. Find value of cos(255degrees)cos(105degrees) root3 - 2 / 4 3. cos(pi/12) - cos(5pi/12) Is it root3/4? 4. Use the appropriate sum-to-product formula to rewrite the expression sin6x - sin9x I don't really understand
  75. precalc

    Find the exact value of each expression, if it exists: the -1 are representing the inverse functions! (a) sin -1 (-√2/2) (b) cos−1 (−1) (c) sin( 􏰀sin−1 (π)􏰁) (d) cos−1􏰀(cos􏰀(−4π􏰁􏰁/ 3)) (e) tan−1 (tan(0.6)) (f) cos−1(
  76. Math(answer check)

    1. Find the modulus and argument of the following complex numbers, and write them in trigonometric form: a. 5 – 8i Answer = Sqrt{89} ( cos (-1.01219701) + i sin ( -1.01219701)) b. –1 – i answer = Sqrt2 (cos (5pi/4) + i sin (5pi/4)) c. –5 + 12i
  77. 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)
  78. math

    How would you establish this identity: (1+sec(beta))/(sec(beta))=(sin^2(beta))/(1-cos(beta)) on the right, sin^2 = 1-cos^2, that factor to 1-cos * `1+cos, then the denominator makes the entire right side 1+cosB which is 1+1/sec which is 1/sec (sec+1) qed
  79. Calculus

    how do you solve this trig identity? i don't get it at all! cos(a+b)cos(a-b)=cos^2a-cos^2b-1
  80. math

    3 cos^2 𝛼 + 2 cos^2 𝛽 =4 3 sin 2 𝛼 − 2sin 2 𝛽=0 Find the values of cos 2𝛼 and cos 2𝛽.
  81. calc

    Where do I start to prove this identity: sinx/cosx= 1-cos2x/sin2x please help!! Hint: Fractions are evil. Get rid of them. Well, cos2x = cos2x - sin2x, so 1-coscx = 1 - cos2x - sin2x = 1 - cos2x + sin2x You should be able to simplify this to 2*something
  82. math

    A trigonmetric polynomial of order n is t(x) = c0 + c1 * cos x + c2 * cos 2x + ... + cn * cos nx + d1 * sin x + d2 * sin 2x + ... + dn * sin nx The output vector space of such a function has the vector basis: { 1, cos x, cos 2x, ..., cos nx, sin x, sin 2x,
  83. Calculus

    Find the exact value of the slope of the line which is tangent to the curve given by the equation r = 2 + cos θ at theta equals pi over 2 . You must show your work. (10 points) Please check if this is right. I put a lot of work into this please check! x=
  84. Physics

    What should be the angle between two vectors of magnitudes 3.20 and 5.70 units, so that their resultant has a magnitude of 6.10 units? Cos x = (b^2 + c^2 - a^2) / 2bc Cos x = (3.2^2 + 5.7^2 - 6.1^2) / (2 * 3.2 * 5.7) Cos x = 5.52/36.48 Cos x = 0.15 x =
  85. Trigonometric

    Consider the following simultaneous equations: 3 cos^2 𝛼 + 2 cos^2 𝛽 =4 3 sin^2 𝛼 − 2sin^2 𝛽=0 *Find the values of cos 2𝛼 and cos 2𝛽. *Hence solve for 𝛼𝛼 and 𝛽𝛽. Where 0°≤𝛼𝛼≤360° and 0°≤𝛽𝛽≤360°.
  86. Trigonometric

    Consider the following simultaneous equations: 3 cos^2 𝛼 + 2 cos^2 𝛽 =4 3 sin^2 𝛼 − 2sin^2 𝛽=0 *Find the values of cos 2𝛼 and cos 2𝛽. *Hence solve for 𝛼 and 𝛽. Where 0°≤𝛼≤360° and 0°≤𝛽≤360°.
  87. Trignometry

    Write the complex number in the form a=bi √(3)(cos π/3 + isin π/3)
  88. Maths

    Given that a complex number Z. = 1 + cos 2@ + isin 2@. Calculate its argument
  89. PRECALC

    solve the equation 1. cos(θ) − sin(θ) = 1 2.2 cos(θ) tan(θ) + tan(θ) = 1 + 2 cos(θ) 3. sin(θ) cos(3θ) + cos(θ) sin(3θ) = 0 4. sin(2θ) cos(θ) − cos(2θ) sin(θ) = 1/2 5. cos(2θ) + cos(θ) = 2 6. cos(2θ) + sin2(θ) = 0
  90. Maths- complex numbers

    Find tan(3 theta) in terms of tan theta Use the formula tan (a + b) = (tan a + tan b)/[1 - tan a tan b) in two steps. First, let a = b = theta and get a formula for tan (2 theta). tan (2 theta) = 2 tan theta/[(1 - tan theta)^2] Then write down the equation
  91. 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
  92. Calculus re-post

    Does anybody know how to solve this question? a) Find the arc length function for the curve measured from the point P in the direction of increasing t from P and then reparametrize the curve with respect to arc length starting from P. b) Find the point 4
  93. Trig (math)

    1.) Write the complex number in trigonometric form r(cos theta + i sin theta) with theta in the interval [0°, 360°). 9 sqrt 3 + 9i 2.) Find the product. Write the product in rectangular form, using exact values. [4 cis 30°] [5 cis 120°] 3.) [4(cos
  94. Pre-Cal

    1) Verify the identity cos^2 B - sin^2 B = 2 cos^2 B -1 I know that cos^2 B - sin^2 B = 2 cos^2 B -1 by the double angle formula but I do not know how to show this.
  95. Precalculus

    Use one of the identities cos(t + 2πk) = cos t or sin(t + 2πk) = sin t to evaluate each expression. (Enter your answers in exact form.) (a) sin(19π/4) (b) sin(−19π/4) (c) cos(11π) (d) cos(53π/4) (e) tan(−3π/4) (f) cos(π/4) (g) sec(π/6+ 2π)
  96. Math - Trigonometry

    Let f(x) be a polynomial such that f(cos theta) = cos(4 theta) for all \theta. Find f(x). (This is essentially the same as finding cos(4 theta) in terms of cos theta; we structure the problem this way so that you can answer as a polynomial. Be sure to
  97. 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
  98. 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
  99. Math

    cos(tan + cot) = csc only simplify one side to equal csc so far I got this far: [((cos)(sin))/(cos)] + [((cos)(cos))/(sin)] = csc I don't know what to do next
  100. Math

    The graph of f(x), a trigonometric function, and the graph of g(x) = c intersect at n points over the interval 0

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