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° &lt; A < 360°. If sin ( A ) = − 1/3 with A in QII then find cos A/2.

Answer 1

Answer:

Step-by-step explanation:

Given that angle A is in IV quadrant

So A/2 would be in II quadrant.

sin A = -1/3

cos A = $\sqrt{1-sin^2 A} =\frac{2\sqrt{2} }{3}$

(cos A is positive since in IV quadrant)

Using this we can find cos A/2

$cosA = 2cos^2 \frac{A}{2} -1\\Or cos \frac{A}{2} =-\sqrt{\frac{1+cosA}{2} } =-\sqrt{\frac{3+2\sqrt{2} }{6} }$