SOLUTION: Use a double- or half-angle identity to find the exact value of each trigonometric expression below if csc x = 4 and 90 degrees < x

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Question 831733: Use a double- or half-angle identity to find the exact value of each trigonometric expression below if csc x = 4 and 90 degrees < x < 180 degrees
a) sin x/2
b) cos x/2
c) tan x/2

Answer by lwsshak3(11628) (Show Source):
You can put this solution on YOUR website!
Use a double- or half-angle identity to find the exact value of each trigonometric expression below if csc x = 4 and 90 degrees < x < 180 degrees
a) sin x/2
b) cos x/2
c) tan x/2
***
cscx=4
sinx=1/4
cosx=-√(1-sin^2x)=-√(1-(1/16))=-√(15/16)=-√15/4
note: cos<0,sin>0 in quadrant II
..
sin(x/2)=
..
cos(x/2)=
..
tan(x/2)=
..
Calculator check:
sinx=1/4
x≈165.52˚ in quadrant II
x/2≈82.76˚
..
sin(x/2)≈sin(82.76)≈0.9920..
exact value=√(4+√15)/8≈0.9920..
..
cos(x/2)≈cos(82.76)≈0.1260..
exact value=√(4-√15)/8≈0.1260..
..
tan(x/2)=tan(82.76)≈7.872..
exact value=1/(4-√15)≈7.872..

SOLUTION: Use a double- or half-angle identity to find the exact value of each trigonometric expression below if csc x = 4 and 90 degrees < x < 180 degrees a) sin x/2 b) cos x/2 c)