Answer:
<h2>
cos (α + β) = 0.9196</h2>
Step-by-step explanation:
Given sin α = –4∕5 and sin β = 1∕2
To get α from sin α = –4∕5,
α = arcsin(-4/5)
α = arcsin (-0.8)
α = -53.13°
If angle α is in quadrant III, then α = 180+53.13 = 233.13° (sin is negative in the 3rd quadrant)
Similarly for sin β = 1∕2
β = arcsin(1/2)
β = arcsin(0.5)
β = 30°
Since β is in quadrant II, β = 180-30 = 150°
To find cos (α + β). where α = 233.13° and β = 30°
cos (α + β)= cos (233.13 + 150)
= cos 383.13°
cos (α + β) = 0.9196
