Question

given that sine theta = 0, and cosine theta is less than zero, find the exact values of the other two trig functions

Answer 1

Below.

Explanation:

The tangent is 0.

The secant is -1.

The cosecant and cotangent are undefined.

Answer 2

θ = π + periods of 2π

Sin (π + 2π) = 0

Cos (π + 2π) = -1

Tan (π + 2π) = 0

Explanation:

Sin (θ)=0 implies that θ only can be 0 or π plus periods of 2π:

θ = 0+2π

θ = π+2π

For Cos(θ) the values only can be:

Cos (0+2π) = 1 and

Cos (π+2π) = -1

from this, only Cos (π+2π) < 0

So θ only can be θ=π+2π