SOLUTION: If cos theta = - 4/5 and 180degree < theta < 270degree, use trigonometric identities to find the exact value of sin 2theta.

Question 753085: If cos theta = - 4/5 and 180degree < theta < 270degree, use trigonometric identities to find the exact value of sin 2theta.
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
If cos theta = - 4/5 and 180degree < theta < 270degree, use trigonometric identities to find the exact value of sin 2theta.
**
sin2x=2sinxcosx
given cosx=-4/5 (in Q3 where cos and sin<0)
sinx=-3/5 (working with 3-4-5 reference right triangle
sin2x=2*-4/5*-3/5=24/25
..
check with calculator:
cosx=-4/5 in Q3
x≈36.87�+180�≈216.87�
2x≈433.74� (Q1 where sin>0)
sin2x=sin(433.74�)≈0.9600..
exact value=24/25≈0.9600..

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