Question

Given sin theta= -3/5 and csc=-5/3 in quadrant III, find the value of other trigonometric functions using a Pythagorean Identity.

Part I: Find the value of cosθ and secθ.


Part II: Using your answers from Part I, find the value of tanθ.

Answer 1

cos θ = -4/5

sec θ = -5/4

tan θ = 3/4

Explanation:

Answer 2

cos θ = -4/5

sec θ = -5/4

tan θ = 3/4

Explanation:

sin²θ + cos²θ = 1

(-3/5)² + cos²θ = 1

9/25 + cos²θ = 1

cos²θ = 16/25

cos θ = ±4/5

Since θ is in quadrant III, cos θ < 0. So cos θ = -4/5.

sec θ = 1 / cos θ

sec θ = -5/4

tan θ = sin θ / cos θ

tan θ = (-3/5) / (-4/5)

tan θ = (-3/5) (-5/4)

tan θ = 3/4