SOLUTION: If cos theta = - 4/5 and 180degree < theta < 270degree, use trigonometric identities to find the exact value of sin 2theta.
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-> SOLUTION: If cos theta = - 4/5 and 180degree < theta < 270degree, use trigonometric identities to find the exact value of sin 2theta.
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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.
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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≈36.87º+180º≈216.87º
2x≈433.74º (Q1 where sin>0)
sin2x=sin(433.74º)≈0.9600..
exact value=24/25≈0.9600..
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