Question

ngles α and β are angles in standard position such that:α terminates in Quadrant III and sinα = -5/13 β terminates in Quadrant II and tanβ = -8/13 Find cos(α - β).

Answer 1

0.5848

Explanation:

Sin α=-5/13--> arcsin(-5/13)=α and we know that α is in quadrant III and because of trigonometry properties we know that sinα can be negative just in quadrant III and IV. There are two options so we choose the option of quadrant III. α≅202,6°

Tanβ=-8/13---> arctang(-8/13)=β and we know that β is in quadrant II and because of trigonometry properties we know that tanβ can be negative just in quadrant II and IV. There are two options so we choose the option of quadrant II. β≅148,39°

cos(α-β)=cos(202,6°-148,39)≅0.5848