Find tan(t) ,sin(t) when cos(t)= -3/5

Question

If cos(t)= -3/5  and t is in Quadrant III, find

a) sin(t)

b) tan(t)

Answer 1

Given that cos(t) = -3/5

a) sin(t)

Then sin²(t) + cos²(t) = 1

Substitute cos(t) value

sin²(t)+ ( -3/5)²= 1

sin²(t) = 1- 9/25

sin(t) = √ 16/25

Therefore sin(t) = 4/5

b) tan(t)

tan(t)  = sin(t)/cos(t)

(4/5)/(-3/5) = - 4/3

Therefore tan(t) = - 4/3

Therefore sin(t) = 4/5 and tan(t) = -4/3.

 

 

Comments

The value of sin(θ) is negative and tan(θ) is positive in third quadrant.

Therefore, sin(t) = - 4/5 and tan(t) = 4/3.