SOLUTION: If cos&#952; = -2/3, and 450 degrees < &#952; < 540 degrees, find: A) Exact value of cos(1/2)&#952; B) Exact value of tan(2&#952;)

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Question 964583: If cosθ = -2/3, and 450 degrees < θ < 540 degrees, find:
A) Exact value of cos(1/2)θ
B) Exact value of tan(2θ)

Answer by lwsshak3(11628)   (Show Source): You can put this solution on YOUR website!
If cosθ = -2/3, and 450 degrees < θ < 540 degrees, find:
A) Exact value of cos(1/2)θ
B) Exact value of tan(2θ)
***


..
sin(2x)=2sinxcosx=2sqrt(5)/3*-2/3=-(4√5)/9
cos(2x)=cos^2(x)-sin^2(x)=4/9-5/9=-1/9
tan(2x)=sin(2x)/cos(2x)=4√5
..
check:
cosx=-2/3
x=491.81˚
2x=983.62˚
x/2=245.91
cos(x/2)≈cos(245.91)≈-0.4082
exact value as computed above=√(1/6)≈-0.4082
tan(2x)=tan(983.62)≈8.94
exact value as computed above=4√5≈8.94

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