Question Detail
Question
If tan α = 4/3, α lies in quadrant III, and cos β = 20/29, β lies in quadrant II. Find sin(α+β).
Correct Answer
Option C is the correct answer.
Detailed Explanation
In quadrant III, tan α = 4/3 means sin α = -4/5, cos α = -3/5. In quadrant II, cos β = 20/29 means sin β = √(1-400/841) = √(441/841) = 21/29, positive in quadrant II. Then sin(α+β) = sin α cos β + cos α sin β = (-4/5)(20/29) + (-3/5)(21/29) = (-80/145) + (-63/145) = -143/145.
Hint
Determine the signs of trigonometric functions in each quadrant.