I cannot figure this problem out!?

Question

Use a half-angle formula to determine the value of (7pi/8).

I keep getting sqrt((2)+sqrt(2))/2.....but that's wrong!

sorry..it's cos(7pi/8)

Answer 1

The formula is:

cos t/2 = ±√((1 + cos t) / 2)

So the angle you're taking half of is 7pi/4, which 45 degrees in the 4th quadrant. 7pi/8 is in the 2nd quadrant, so you want the negative solution.

cos 7pi/4 = cos -pi/4 = √2/2

cos 7pi/8 = -√((1 + √2/2)/2)

=-√(1/2((2+√2)/2)
=-√(2+√2)/4
=-1/2√(2+√2)

...so what's wrong with your answer? other than the missing - sign.