Suppose that the terminal side of angle a lies in Quadrant I

Suppose that the terminal side of angle a lies in Quadrant IV and the teminal side of angle B lies in Quadrant III. If sin a = -1/4 and cosB = -5/13, find the exact value of tan (a+b)

Solution

angle A lies in Quadrant IV and the teminal side of angle B lies in Quadrant III

sin A = -1/4 and cosB = -5/13

tanA = -1/sqrt15

cosB = -5/13

tanB = 12/5

tan(A+B) = (tanA +tanB)/( 1-tanAtanB) = ( -1/sqrt15 +12/5)/( 1- (- 12/5sqrt15) )

= ( -5 + 12sqrt(15) )/( 5sqrt15 + 12)

= (12sqrt(15) -5)/( 5sqrt15 + 12)