1. Questions

Pre-Calculus-check answers

If cos theta = 0.8 and 270<theta<360, find the exact value of sin 2theta

a) -0.96
b) -0.6
c) 0.96
d) 0.28

Answer: b

2) If csc theta = -5/3, and theta has its terminal side in Quadrant III, find the exact value of tan 2theta

a)24/25
b) 7/25
c) 24/7
d) -7/25

Thanks

  1. 👍
  2. 👎
  3. 👁
  4. ℹ️
  5. 🚩
Lucy

  1. 1) cosθ=0.8 , θ is in fourth quadrant
    θ= cos^(-1)0.8=36.86989765 + 270=306.87

    so , sin 2θ= sin2(306.87)= -0.96
    answer : a

    1. 👍
    2. 👎
    3. ℹ️
    4. 🚩
    Mohamed

  2. 2) csc Ø = -5/3, then sin Ø = -3/5 and is in III

    the cos Ø = -4/5

    so tan 2Ø = sin 2Ø/cos 2Ø
    = 2sinØcosØ/(cos^2 Ø - sin^2 Ø)
    =2(-3/5)(-4/5)/(16/25 - 9/25)
    = 24/7

    1. 👍
    2. 👎
    3. ℹ️
    4. 🚩
    Reiny

  4. 1) cscθ = (-5/3) , θ is in third quadrant
    1/sinθ = (-5/3) => sinθ= -3/5
    θ= -36.8699
    θ is in third quadrant
    so θ = 36.8669+180 = 216.8669

    tan2θ = tan2(216.8669) = 3.42724 = 24/7

    answer : c

    1. 👍
    2. 👎
    3. ℹ️
    4. 🚩
    Mohamed

  5. When a trig question asks for "exact" value, a calculator is not to be used, and all work has to be shown with exact values.

    24/7 is not equal to 3.42724

    1. 👍
    2. 👎
    3. ℹ️
    4. 🚩
    Reiny

  6. thanks for note Reiny .

    1. 👍
    2. 👎
    3. ℹ️
    4. 🚩
    Mohamed

Respond to this Question

First Name

Your Response

Similar Questions

  1. 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

  2. Algebra 2

    Simplify the trigonometric expression. sin^2 theta / 1-cos theta A. 1+cos theta B. sin theta C. 1-sin theta / cos theta D. 1+sin theta / cos theta

  3. Algebra 2

    Which cosine function has maximum of 4, a minimum of -4, and a period of 2pi/3? A. y=4 cos 3 theta B. y= 4 cos 2 theta/3 C. y=4 cos theta/3 D. y=4 cos 3 theta

  4. Pre-Calculus

    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

  1. Algebra2

    solve the equation cos theta - tan theta * cos theta = 0 for 0< theta < 2 pi My answer is pi/4,5pi/4

  2. 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.)

  3. 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

  4. 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.

  1. 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

  2. Math

    if tan theta = 3/4 and 180 degrees ≤ 0 ≤ 270 degrees determine with the aid of a complete sketch 1. sin theta 2. cos(180 +theta) 3. angle theta

  3. 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

  4. related rates with work shown

    this is a relate rates problem in calculus in a right triangle, the hypotenuse is 5 and the vertical side is x and the angle is theta. so if theta increases at a constant rate of 3 radians per minute, at what rate is x increasing

View more similar questions or ask a new question.