SOLUTION: Given that tan&#945;=8/15 (180°<&#945;<270°). Find Cos(&#945;/2)

Algebra ->  Trigonometry-basics -> SOLUTION: Given that tan&#945;=8/15 (180°<&#945;<270°). Find Cos(&#945;/2)      Log On


   

Question 1112371: Given that tanα=8/15 (180°<α<270°). Find Cos(α/2)
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
alpha is in III quadrant
use Pythagoras theorem
sqrt%288%5E2%2B15%5E2%29 = hypotenuse =17
cosalpha = 15/17
2cos%5E2%28%28alpha%29%2F2%29= 1%2Bcos%28alpha%29
2cos%5E2%28%28alpha%29%2F2%29= 1%2B%2815%2F17%29

2cos%5E2%28%28alpha%29%2F2%29= 32%2F17%29

cos%5E2%28%28alpha%29%2F2%29= 16%2F17%29
cos alpha = 4%2Fsqrt%2817%29
alpha is in III quadrant so ....