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

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  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

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  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

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  3. 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

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  4. 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

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  5. thanks for note Reiny .

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