Question

Angles α and β are angles in standard position such that: α terminates in Quadrant I and sinα = 3/5, β terminates in Quadrant III and tanβ = 5/12. Find sin(α - β).

A. -56/65
B. -16/65
C. 16/65
D. 56/65

Answer 1

sin(α - β) = sinαcosβ - cosαsinβ, sin(α - β) = -59/60

Step-by-step explanation:

To find sin(α - β), we can use the formula:

sin(α - β) = sinαcosβ - cosαsinβ

We know that sinα = 3/5 and cosα is positive in Quadrant I. Therefore, cosα = √(1 - sin²α) = √(1 - (3/5)²) = √(1 - 9/25) = √(16/25) = 4/5.

We also know that tanβ = 5/12 and tanβ is negative in Quadrant III. Therefore, cosβ = -√(1 + tan²β) = -√(1 + (5/12)²) = -√(1 + 25/144) = -√(169/144) = -13/12.

Plugging the values into the formula, we get:

sin(α - β) = (3/5)(-13/12) - (4/5)(5/12) = -39/60 - 20/60 = -59/60

So, sin(α - β) = -59/60