sin ( α ) = 2/7 and cos ( β ) = − 5/6 Both angles terminate in Quadrant II. What does sin ( α + β ) =? And What does cos ( α + β ) =?

Answer 1

Sketch the two triangles in 2nd quadrant and find missing sides with Pythagorean Theorem: For angle α, adjacent = -√45 = -3√5; for angle β, opposite = √11.

sin(α+β) = sin α cos β + cos α sin β = (2/7)(-5/6) + (-3√5 /7)(√11 /6) = -(10 + 3√55)/42 = -0.7678.

cos(α+β) = cos α cos β - sin α sin β = (-3√5 /7)(-5/6) - (2/7)(√11 /6) = (15√5 - 2√11)/42 = +0.6407.