Question 594805: Use a half-way identity to find exact value for sin(theta),cos(theta), and tan(theta), theta= 75 degrees.
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! Use a half-way identity to find exact value for sin(theta),cos(theta), and tan(theta), theta= 75 degrees.
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Half-Angle Formulas:
sin x/2=±√[(1-cos x)/2)]
cos x/2=±√[(1+cos x)/2)]
tan x/2=(sin x)/(1+cos x)
..
sin 75º=sin 150/2=±√[(1-cos 150)/2)] (use positive root because 75º is in quadrant I where sin>0)
=√[(1-(-√3/2))/2)]
=√[(1+√3/2)/2)]
=√.933≈.966
..
cos 75º=cos 150/2=±√[(1+cos 150)/2)] (use positive root because 75º is in quadrant I where cos>0)
=√[(1+(-√3/2))/2)]
=√[(1-√3/2)/2)]
=√.067≈.259
..
tan 75º=tan 150/2=sin 150/(1+cos 150)
=(1/2)/(1+(-√3/2))
≈3.73
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