What is the value of tan(theta) on an interval?

Question

When (π / 2) < theta < (3π / 4),

What is the value of tan(theta)?

Answer 1

You are right, RU, tan(θ) would be in (-∞, -1)

Answer 2

tan(theta) = sin(theta)/cos(theta).

As theta approaches PI/2 sin(theta) converges to 1 and cosine(theta) converges to 0, so tan(theta) converges to positive infinity.

At theta = 3PI/4, sin(theta) = -cos(theta), so as theta converges to 3PI/4, tan(theta) converges to -1.

so -1 < tan(theta) < infinity for PI/2 < theta < 3*PI/4