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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

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
d) -7/25

Thanks

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

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)

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

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

• note to Mohamed -

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

• note to Mohamed -

thanks for note Reiny .

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