SOLUTION: Suppose sin(X) = 4/5, and the terminal side of X is in quadrant II. A.Find cos(x). B.Use a double-angle formula to find sin(2x). C.Use a double-angle formula to find cos(2x)

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Question 927015: Suppose sin(X) = 4/5, and the terminal side of X is in quadrant II.
A.Find cos(x).
B.Use a double-angle formula to find sin(2x).
C.Use a double-angle formula to find cos(2x)
Answer by lwsshak3(11628) (Show Source):
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Suppose sin(X) = 4/5, and the terminal side of X is in quadrant II.
A.Find cos(x)=-3/5 (working with a (3-4-5) reference right triangle in quadrant II where sin>0, cos<0
B.Use a double-angle formula to find sin(2x)=2sinxcosx=2*4/5*-3/5=-24/25
C.Use a double-angle formula to find cos(2x)=cos^2(x)-sin^2(x)=9/25-16/25=-7/25
check:
sinx=4/5
x≈126.87˚
2x=253.74
sin(2x)=sin(253.74)≈-0.9600
exact value as computed=-24/25=-0.9600
cos(2x)=cos(253.74)≈-0.2800
exact value as computed=-7/25=-0.2800