Question

For the following problem, assume that all given angles are in simplest form, so that if A is in QIV you may assume that 270° < A < 360°. If sin ( A ) = − 1/3 with A in QII then find cos A/2.

Answer 1

Explanation:

Given that angle A is in IV quadrant

So A/2 would be in II quadrant.

sin A = -1/3

cos A =
`√(1-sin^2 A) =(2√(2) )/(3)`

(cos A is positive since in IV quadrant)

Using this we can find cos A/2

`cosA = 2cos^2 (A)/(2) -1\\Or cos (A)/(2) =-\sqrt{(1+cosA)/(2) } =-\sqrt{(3+2√(2) )/(6) }`