SOLUTION: Find the values of the six trigonometric functions if the conditions provided hold. cos(2θ) = 1/√2 and 90° ≤ θ ≤ 180°

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Question 1205057: Find the values of the six trigonometric functions if the conditions provided hold.
cos(2θ) = 1/√2 and 90° ≤ θ ≤ 180°
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

cos%282theta%29=1%2Fsqrt%282%29 and 90+%3C=+theta+%3C=+180°
cos%282theta%29=sqrt%282%29%2F2
first, we need to find angle theta
using unit circle you see that there are two angles whose cosine is sqrt%282%29%2F2: 45° or 315°

We need theta in the second quadrant, so use 315°.

if cos%28315%29+=+sqrt%282%29%2F2, then 2theta+=+315+ =>theta=+157.5°
So the angle we are looking for in the given range is 157.5°
.Now just find the values of the six trigonometric functions :
sin%28157.5%29=0.3827
cos%28157.5%29=-0.9239
tan%28157.5%29=-0.4142
cot%28157.5%29=-2.4142
sec%28157.5%29=-1.0824
csc%28157.5%29=2.6131