# If x a third quadrant angle and y an acute angle such that cos x=-(3/5) and sec y= (3/2) ,find the exact value of sin(x-y) , exact value of tan(x-y) and quadrant containing (x-y)?

##### 1 Answer

Find sin (x - y), knowing cos x = -3/5 and sec y = 3/2

#### Explanation:

Apply the trig identity:

sin (x - y) = sin x.cos y - sin y.cos x

Apply trig identity:

The arc (x - y) is located in Quadrant III since its cos and its sin are both negative.

Check by calculator:

Arc (x - y) = 233.14 - 48.19 = 184.95 deg --> sin (x - y) = -0.09