8. Angle α is in quadrant III, and angle β is in quadrant II. If sin α = –4∕5 and sin β = 1∕2, find cos (α + β).

D

Step-by-step explanation:

Using the addition formula for cosine

cos(α + β) = cosαcosβ - sinαsinβ

Given α in quadrant 3 then and sinα = - = , then

cosα < 0 in the third quadrant

The adjacent side of the triangle = 3  since 3- 4- 5 right triangle

Thus

cosα = = -

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Given β in second quadrant and sinβ = = , then

cosβ < 0 in the second quadrant

The adjacent side of the triangle = since 1- - 2 right triangle

Thus

cosβ = = -

Hence

cos(α + β )

= ( - × - ) - (- × )

= +

= → D