Question

Angles 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 = - 8/15

Find cos(α - β)

-220/221
-140/221
140/221
220/221

Answer 1

140/221.

Explanation:

For the triangle containing angle α:

The adjacent side is -√(13^2-5^2) = -12.

For the triangle containing angle β:

Hypotenuse = √(-8)^2 + (15)^2) = 17.

cos(α - β) = cos α cos β + sin α sin β

= ((-12/13) * (-15/17) + (-5/13)* (8/17)

= 180/221 + - 40/221

= 140/221.