# State the amplitude of the following functions: a) y = cos theta b) y = 1/2cos theta c) y = -2cos theta

63,639 results

1. ### Trigonometry

State the amplitude of the following functions: a) y = cos theta b) y = 1/2cos theta c) y = -2cos theta
2. ### Trigonometry

Prove the following identities: 1. (tan theta - sin theta)^2 + (1-cos theta)^2 = (1-sec theta) ^2 2. (1-2cos^2 theta) / sin theta cos theta = tan theta - cot theta 3. (sin theta + cos theta ) ^2 + (sin theta - cos theta ) ^2 = 2 Thank you so much! :)
3. ### Trigonometry

Prove the following identities: 1. (tan theta - sin theta)^2 + (1-cos theta)^2 = (1-sec theta) ^2 2. (1-2cos^2 theta) / sin theta cos theta = tan theta - cot theta 3. (sin theta + cos theta ) ^2 + (sin theta - cos theta ) ^2 = 2 Thank you so much! :)
4. ### Trig

Which expression equivalent to: cos(theta + pi/2). A)cos theta B)-cos theta C)sin theta D)-sin theta my book doesnt give examples of this but my crack at it would be C b/c distributive property? and 2cos theta = sin theta
5. ### Math

Which of the following functions have a vertical asymptote for values of theta such that cos theta = 1? Select two answers. y = sin theta y = cos theta y = tan theta y = sec theta y = csc theta y = cot theta I know what all these functions look like, but I don't know what the ...
6. ### Trig

Solve the following interval 0<_ (less than or equal to)0(Theta)<2pi: 1. sin0(theta) + sin2 0(theta) = 0 2. 2cos^20 (theta) + cos0 (theta) -1 = 0
7. ### Calculus

I wanted to confirm that I solved these problems correctly (we had to convert the polar curves to Cartesian equations). 1.rcos(theta)=1 x=1 2.r=2*sin(theta)+2*cos(theta) r^2=2rsin(theta)+2rcos(theta) x^2+y^2=2y+2x (a little unsure what do next if this is correct) 3.r=tan(theta...
8. ### Trigonometry

I am having problems with proving identities that has a number and an exponent with it. Like: *2cosxcsc2x = cscx *sin^2 2x = 4sin^2 x cos^2 x *cot2(theta)=csc(theta)-2sin(theta)/2cos(theta)
9. ### Precalculus

2cos^2(theta) + Sin(theta)=1 I know I have to use the quadratic formula but i'm having trouble after I convert the Cos^2(theta) to (1-Sin^2(theta))
10. ### Algebra2

The function f(theta) and g (theta) are sine functions where f(0)=g(0)=0. The amplitude of f (theta) is twice the amplitude of g(theta). The period of f(theta) is one-half the period of g(theta). If g (theta) has a period of 2pi and fpi/4=4. Write the function rule for g(theta...
11. ### tri

solve exactly over the indicated interval: 2cos^2(theta)=cos(theta), 0<theta<2pi
12. ### math;)

Julia wants to simplify the term sec^2 theta-1/cot^2 theta+1 in a trigonometric identity that she is proving. Which of the following identities should use to help her? Select all that apply. (2 ANSWERS) a. sin^2 theta+cos^2 theta=1 b. sec^2 theta-tan^2 theta=1 c. sec theta=1/...
13. ### Precalculus

Circle O below has radius 1. Eight segment lengths are labeled with lowercase letters. Six of these equal a trigonometric function of theta. Your answer to this problem should be a six letter sequence whose letters represent the segment lengths that equal the following ...
14. ### precalc h

sin(theta)/1-cos(theta) + 1-cos(theta)/sin(theta) = 2csc(theta) That question makes absolutely no sense.. could someone help me? or lead me in the direction to figuring it out? and.. (Beside the trig functions is theta) 1+1/cos = tan^2/sec-1
15. ### Physics

An object is shot at 20m/s at an angle theta. The object lands 24m away. What is the angle? Can you check if I am doing this right? I had v(initial) = 20 m/s g = 9.8 m/s^2 x = 24m 1st I solved for time: x = v(initial) t x = v(initial) cos(theta) t 24 = 20 cos(theta) t 24 / [20...
16. ### Pre Cal

2cos 4theta + 1 = 0 i know how to find the degrees (the last step of the problem), but i don't know how to start the problem. Could someone please show me the steps? I assume you mean cos (4 theta) and not (cos theta)^4 cos (4 theta) = -1/2 The angles with a cosine equal to -1...
17. ### Pre Calc.

Use the sum or difference identity to find the exact value of sin255 degrees. My answer: (-sqrt(2)- sqrt(6)) / (4) Find the value of tan (alpha-beta), if cos alpha= -3/5, sin beta= 5/13, 90<alpha<180, and 90<beta<180. My answer: -33/56 Which expression is ...
18. ### Algebra II

Multiple Choice Which expression is NOT equivalent to 1? (theta) means 0 with dash in it. A.)sin^2 (theta)+cot^2 (theta) sin^2 (theta) B.)(sin^(theta))/(1-cos(theta))-cos(theta) C,)sec^2 (theta)+ tan^2 (theta) D.)(cot^2(theta) sin^2 (theta))/(cos^2(theta))
19. ### calculus

Find circumference of the circle r=2acos theta. s= Int (0 to 2pi) of Sqrt(4a^2cos^2 theta+4a^2sin^2 theta)d theta =Int (0 to 2pi)2a*Int theta d theta =2a(2pi-0)=4a*pi Book shows 2a*pi. Am I wrong somewhere?
20. ### trig

If sin theta is equal to 5/13 and theta is an angle in quadrant II find the value of cos theta, sec theta, tan theta, csc theta, cot theta.
21. ### Algebra II

Which of the following expressions are not equal to 1? A) sin^2 theta + cot^2 theta sin^2 theta B) (sin^2 theta/1-cos theta)-cos theta C) sec^2 theta + tan^2 theta D) cot^2 theta sin^2 theta/cos^2theta Answer: D
22. ### Trigonometry

Thank you STEVE!!!!! Suppose that Cos (theta) = 1/square root 2 if 0<equal to theta , pi/2 then sin(theta) = tan (theta) = If 3pi/2 less than equal to theta , 2pi then sin(theta) = tan (theta) = I know the trig functions but I feel like I am missing something here. cos (...
23. ### math

knowing that 2(theta) can be written as theta + theta, find the expression for sin2(theta) and cos2(theta). Is it 2sin(theta)cos(theta)?
24. ### Precalculus 2

Similiarly to a question I asked previously I took the same approach. the problem is: what value(s) of theta solve the following equation? cos(theta)sin(theta) - 2 cos(theta) = 0? I let Cos theta = X and sin theta = X unfortunately I end up with something completely odd. Can ...
25. ### Mathamatics

Solve the following trigonometry identities. a) 1-cos2(theta) = sin(theta)cos(theta)/cot(theta) b) (1-cos2(theta))(1-tan2(theta))=sin2(theta)-2sin4(theta)/1-sin2(theta) *its supposed to be cos to the power of two, sin to the power of four, etc. There is also supposed to be a ...
26. ### trigonomtry

can you correct the rest for me please? Express each as a function of theta: a. sin (270deg + theta)= cos theta b. cos (pi + theta)= -cos theta c. tan (810 + theta)= ????? d. sin (theta - 180)= -sin theta
27. ### trigonometry

can you correct the rest for me please? Express each as a function of theta: a. sin (270deg + theta)= cos theta b. cos (pi + theta)= -cos theta c. tan (810 + theta)= ????? d. sin (theta - 180)= -sin theta
28. ### trigonometry

can you correct the rest for me please? Express each as a function of theta: a. sin (270deg + theta)= cos theta b. cos (pi + theta)= -cos theta c. tan (810 + theta)= ????? d. sin (theta - 180)= -sin theta
29. ### math

prove 3cos theta - cos3theta = 2cos theta cos2theta + 4sin theta sin 2theta
30. ### trig

sin theta/2cos theta/2=1/2 sine theta show the identiy and work
31. ### Pre-Calculus Help?

1.) Which of the following polar equations is equivalent to the parametric equations below? x=t^2 y=2t A.) r=4cot(theta)csc(theta) B.) r=4tan(theta)sec(theta) C.) r=tan(theta)sec(theta)/4 D.) r=16cot(theta)csc(theta) 2.) Which polar equation is equivalent to the parametric ...
32. ### Precalculus

Which of the following are trigonometric identities? Select all that apply (there are 3 answers). A cos^2(theta)=sin^2(theta)-1 B sin(theta)=1/csc(theta) C sec(theta)=1/cot(theta) D cot(theta)=cos/sin(theta) E 1+cot^2(theta)=csc^2(theta)
33. ### trig

Hi, I need to find the domain and rnge of the following: 1. X= 1/2 (cos theta + theta sin theta) Y=1/2 (sin theta - theta cos theta) total guess here, but here goes Domain cos theta = +/- 1 and domain sin theta = +/- 1 so domain theta sin theta = 0- +/-infinity so domain of X...
34. ### Trigonometry

determine real numbers a and b so that the expression 8sin^2(theta) + 2cos^2(theta) can be rewritten as asin^2(theta) + b I just need help in how to start it.
35. ### Trigonometry

I don't understand how I'm supposed set the problem up or what theta is... Use the given function value(s), and trigonometric identities (including the cofunction identities), to find the indicated trigonometric functions. sec theta = 5, tan theta 2 * 6^1/2 a) cos theta b) cot...
36. ### math

I have a question I have been working on since yesterday and I am not making this up. I couldn't get the right answer. If sin theta = -2/3, which of the following are possible? A: cos theta= -the sqr rt of 5/3 and tan theta =2/3. B: sec theta = 3/the sqr rt of 5 and tan teta...
37. ### Trigonometry

determine real numbers a and b so that the expression 8sin^2(theta) + 2cos^2(theta) can be rewritten as (a)sin^2(theta) + b? If you can help me out on how to start it would be great.
38. ### Cosine question

cos theta= .5 2cos theta= .5 how do you do this?
39. ### math (trig)

if cos 2 theta = -(1/3) and theta is in Quadrant 2, find sin theta, cos theta, tan theta, and draw triangle theta
40. ### Trigonometrt

Express in functions of theta: a. sin ( 810- theta) b. cot ( theta - 360) c cos (-180- theta)
41. ### Precalculus(NEED HELP ASAP PLEASE!!)

cot(theta)= 3 pi < theta < 3pi/2 Find: sin(theta)= -1 ? cos(theta)= -3 ? tan(theta)= 1/3 ? sec(theta)= -1/3 ? csc(theta)= -1 ? That's what I came up with, but they are not correct, PLEASE help me where I went wrong!!
42. ### Calculus

If cos of theta= -7/12 and theta is in quadrant 2 then find a. tan(theta) cot (theta)= b. csc(theta) tan(theta)= c. sin^2(theta)+ cos^2(theta)=
43. ### math;)

What is a simplified form of the expression (sec^3 theta) - (sec theta/cot^2 theta)? a. 0 b. sec theta-tan theta c. cos theta d. sec theta***** Every time I attempt to work out this problem I end up with one. I know the answer is sec theta, but I do not know how to get there. ...
44. ### math

Hi ! Here is my question: The pythagorean theorem gives the relationships between the sides of a right triangle. The following identities show the relationships between the trigonometric functions of a particular angle. sin^2(theta) + cos^2(theta) = 1 tan^2(theta) + 1 = sec^2(...
45. ### 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 little. Can you clarify ...
46. ### Optimization

min 2x+y subject to: x+y+z=1 and y^2+z^2=4 Any help would greatly be apprecaited. y^2+z^2=4 ---> put y = 2 cos(theta) and z = 2 sin(theta) x+y+z=1 ----> x = 1-2(cos(theta) + sin(theta)) 2x + y = 2 - 2 cos(theta) - 4 sin(theta) It's not difficult to find the minimum of ...
47. ### MATHS TRIGONOMETRY

if 3sin theta =2 and cos greater than 0,with the aid of a diagram determine the value of: a) tan theta b) sin theta/cos theta c) sin^2 theta + cos^2 theta
48. ### math

put these polar equations into cartesians form: 1) theta=135 degrees 2)rcostheta=-1 for #1 is it like: (-1,1)? and for #2, X=-1, but i cant find y, any help is appreciated The slope should be sin(theta)/cos(theta) and the intercept is the origin. x=r*cos(theta) If r=1 we have ...
49. ### math(Trigonometry)

sin 2 theta + cos theta = 0 so, we use sin 2 theta = 2 sin theta cos theta right? but the problem is i'm stuck on (2 sin theta cos theta) + cos theta = 0. What should i do?
50. ### Math

An angle theta satisfies the relation (csc theta)(cos theta)=-1 Give an example of information needed to determine a unique value for theta If sec theta is known to be negative, what is the csc theta value of theta?

Find exact values for all the solutions to the equation cos theta = sqrt 3/2 for -2pi <= theta <= 2pi Theta = Theta = Theta = Theta =
52. ### Math Trig Help

sin theta = x/3, with theta in the first quadrant, find the expression for cos theta and tan theta. Answers will be in algebraic terms of x. Give exact answers with 0 < theta <pi/2 (0 less than or equal to theta, less than or equal to pi/2 Cos theta ? Tan Theta?
53. ### Precalculus check answers help!

1.) Find an expression equivalent to sec theta sin theta cot theta csc theta. tan theta csc theta sec theta ~ sin theta 2.) Find an expression equivalent to cos theta/sin theta . tan theta cot theta ~ sec theta csc theta 3.) Simplify (tan^2 theta + 1)/(tan^2 theta) . csc2 ...
54. ### Precalculus check answers help!

1.) Find an expression equivalent to sec theta sin theta cot theta csc theta. tan theta csc theta sec theta ~ sin theta 2.) Find an expression equivalent to cos theta/sin theta . tan theta cot theta ~ sec theta csc theta 3.) Simplify (tan^2 theta + 1)/(tan^2 theta) . csc2 ...
55. ### trigonometry

I need help in understanding how to identify which identity to use. using this question as an example. Show that tan theta (sin theta+cot theta cos theata)all over cos theta = sec^2 theta. Please explain.
56. ### Math

angle theta is in the standard position and 0'=<theta=<180'. If cos theta = -2/3, find the exact value of sin theta* tan theta.
57. ### Trigonometric Functions

Determine the Value of all six trigonometric functions of theta when given? I need help. This is for my midterm review, if anyone is willing to help, I'd appreciate it. a) sin theta= 3/5 and theta is in quadrant 1. b) tan theta= -2 and theta is in quadrant II c) sec theta = 2 ...

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. Can you clarify if ...
59. ### Calculus

I'm extremely confused on what to do in part a of this question. Consider the curve given by x=3sin(theta), y=1+2cos(theta), 0<=theta<=3pi/2 (a) Eliminate the parameter and find a Cartesian (Rectangular) equation for the curve.
60. ### Math

Justin wants to evaluate 3cot(-5pi/4). Which of the following identities can he use to help him? Select two answers. cot(-theta) = cot(theta) cot(-theta) = -cot(theta) cot(-theta) = cot(-theta) cot(theta + pi) = cot(theta) cot(theta + 2pi) = cot(theta)
61. ### help help helpppp--math

1)Use the definitions sin0(theta) = y/r, cos0(theta) = x/r and/or tan0(theta) = y/x to prove that cot0(theta) = 1/tan0(theta) 2)For all 0(theta) prove: a)cos(t) = 1/sec0(theta) b. sec(t) = 1/cos0(theta)
62. ### trig

If theta is the measure of an angle in standard position with the given conditions, find the quadrant(s) in which the terminal side of theta lies. a) cot theta < 0 b) cos theta > 0 , csc theta < 0
63. ### Math

1)Use the definitions sin0(theta) = y/r, cos0(theta) = x/r and/or tan0(theta) = y/x to prove that cot0(theta) = 1/tan0(theta) 2)For all 0(theta) prove: a)cos(t) = 1/sec0(theta) b. sec(t) = 1/cos0(theta)
64. ### trig

Work out the following identities a) sin theta/cos theta b) tan theta cos theta
65. ### calculus

conic sections prove that the line x-2y+10=0 touches the ellipse 9x^2+64y^2=576 show that the equation of the normal to the ellipse x^2/a^2 + y^2/b^2 = 1 at the point (a cos theta, b sin theta ) is ax sin theta - by cos theta - (a^2-b^2) sin theta cos theta =0
66. ### Trig Identities

Please help...I'm not understanding trig identities and how to manipulate and express these two problems in their associated functions. Thanks a)Express as a function of cos (theta) 2 sin^2(theta) - 1 b)Express as a function of sin (theta) or cos (theta) tan^2(theta) - 2 sec(...
67. ### Calculus

convert to polar: 2xy=3 A. r=sqrt(3sin theta cos theta) B. r=sqrt[(3sin theta cos theta)/2] C. r=[3/(2sin theta cos theta)] D.This cannot be converted without ambiguity.
68. ### Precalculus(NEED HELP ASAP PLEASE!!)

Solve: sin(theta)cos(theta)-sin(theta)−cos(theta)+1 = 0, 0 < or equal to theta < 2pi Solution Set: ____________ ?
69. ### Trigonometry

Okay, I have been given a trigonometric equation to solve (sin^2(theta) + cos(theta) = 2). So far, I have been able to use the Pythagorean identity to get (-cos^2(theta) + cos(theta) - 1 = 0), which I then multiplied by -1 on both sides to get: (cos^2(theta) - cos(theta) + 1...
70. ### math

Another: theta is a second quadrant angle in standard position and tan theta = - (sqrt5)/(2) . Find the exact value of cos theta. I assume I use the equation 1 / cos(theta)^2 = 1 + tan (theta)^2 However how does this work out algebraically?
71. ### 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 for tan (2 theta + ...
72. ### Pre calculus

in the equation r= 5/(sin theta +2cos theta) the letters r and theta represent polar coordinates. Write the equivalent equation using rectangular coordinates. Thanks :)
73. ### science

Sitting on a horizontal track is a mass of 10kg. One end of the track is raised untill the mass just begins to slip. If the coeffieient of static friction is .4 what is the minimum angle at which the mass begins to slip? mgSinTheta = mg*mu*CosTheta (10)(-9.8)sin theta = (10)(-...
74. ### math

Thank You for taking the time to look at this. If x = 2cos^2(theta) and y = sin2(theta), show that (x -1)^2 + y^2=1
75. ### Calculus

Calculate the area of the common interior of r = 2sin(theta) and r = 2cos(theta)
76. ### Diagonalize

construct a nondiagonal 2 x 2 matrix that is diagonalizable but not invertible. Just write down a diagonal matrix with one zero on the diagonal and then apply an orthogonal transformation. E.g. if you start with the matrix: A = [1 ,0 0,1] And take the orthogonal transformation...
77. ### Calculus

Convert the curve to an equation in rectangular coordinates: x=sin theta + 1 y=2cos theta - 1
78. ### Hearne High

Find the exact value of each of the other 5 trigonometric functions for the angle of theta (without finding theta) when cos theta is 3/5
79. ### physics (the algebra bit)

ok my question I'm trying to solve this for a m1 a = m2 g - m2 a - m1 g sin theta - (Mu kinetic)m1 g cos theta my text book gives me this a = (m1 + m2)^-1 (m2 g - m1 g sin theta - (Mu kinetic) m1 g cos theta) ok I don't see how I get to this point tand don't know what to do a...
80. ### precalc

Eliminate the parameter and write the corresponding rectangular equation. X=2cos theta, y=4sin theta
81. ### Trigonometry

Solve: 2cos^2 theta - 3cos theta+ 1= 0 interval [0, 2ð)
82. ### Precalculus(NEED HELP ASAP PLEASE!!)

PLEASE HELP!! csc(theta)= -3/2 3pi/2 < theta < 2pi Find: sin(theta)= _____ ? cos(theta)= _____ ? tan(theta)= _____ ? cot(theta)= _____ ? sec(theta)= _____ ?
83. ### math

Prove the identity cos theta - sin theta / cos theta + sin theta = sec 2 theta - tan 2 theta.
84. ### Trig

Find the exact value of sin2(theta) if cos(theta) = -sqrt 5/3 and 180 < theta < 270. A)-1/9 B)-4 sqrt 5/9 C)1/9 D)4 sqrt 5/9 B? sin^2(theta) + cos^2(theta) = 1 sin^2(theta) = 1 - cos^2(theta) sin^2(theta) = 1 - (sqrt 5/3)^2 sin^2(theta) = 1 - (sqrt 25/9)
85. ### trig

finding the equivalent polar equation 2x+3y=6 I got r=6/2cos(theta)-3sin(theta) can anyone check plz
86. ### 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 write your polynomial ...
87. ### Pre-Calculus

Which is the polar form of the parametric equations x=5cos(theta) and y=5sin(theta) ? a. r= 5(theta) b. r= 5 c. r= 25 cos (theta) sin (theta)***** d. r= 25cos^2 (theta) + 25sin^2 (theta) Which is the polar form of the parametric equations x=4t and y=t^2? a. r= 16 tan (theta) ...
88. ### Calculous

Evaluate sin(theta) and cosine (theta) for the angle theta The graph gives you a point of (0.6,-0.8) on the x y coordinate plane with a radius of what appears to be 1 ( unit circle ) sin (theta) = cos (theta) =
89. ### Precalculus Follow Up 2

Oh now I see your point. I am sorry I should have stated this before. How do I verify that tan^2(theta)/Sec(theta)-1 is somehow the same as 1+cos(theta)/Cos(Theta)?
90. ### Calculus

sec theta 5 need to find cos theta cot theta cot (90-theta) sin theta not sure what to do completely confused on this stuff
91. ### Trigonometry

1. sin^2 theta+cos theta=2 (Hint: Use the Pythagorean identity sin^2 theta+cos theta=1 to replace sin^2 theta in the given equation.) I got no solution
92. ### Trigonometry

Need help solving problems using the Trigonometric Identities: 8cos^4 thet=cos4theta+4cos2theta+3 I am a bit unsure how to solve it. I am aware that the first step I must take is to simplify the problem and then use the Product to Sum formula Nasty one! let's start on the ...
93. ### maths trigonometry

solve the equation (2cos theta +1)(tan theta minus 1)=0 for all values between 0 and 2pii.
94. ### math(Trigonometry)

2cos^2 theta + 5 sin theta - 4 = 0
95. ### trig

If cosecant of theta equals 3 and cosine of theta is less than zero, find sine of theta, cosine of theta, tangent of theta, cotangent of theta and secant of theta
96. ### Calculus

Finding critical numbers g(theta) = 16(theta) - 4tan(theta) I can only get the derivative of g to be g'(theta) = 16 - 4sec^2(theta). Am I supposed to move on to get sec^2(theta) = 4, then sec(theta) = 2?