Pre Calculus

Question

Find the value for cos(x/2) if the following conditions hold: sin(x)=-12/13  and x is in quadrant 3

a) -√17/6

b) -√7/24

c) -√7/6

d) -√17/24

Answer 1

Using the Pythagorean identity, cos²x = 1 - (-12/13)² = 25/169; therefore cos x = - 5/13 (because of Quadrant III).

 

x/2 will be an angle in quadrant II so its cosine will be negative, given by the half-angle formula

cos (x/2) = ±√[½(1+cos x)] = -√[½(1+(-5/13)] = -2/√13 = -.5547

 

I am certain that this is correct (I checked it on the calculator, decimally...) and therefore I say that NONE OF THE ANSWERS a-d is correct.  Because x = 247.38 degrees and you can divide that by 2 and then find the cosine of that, and it's exactly the decimal number -.5547.