Question

Take a moment to think about what tan(θ) represents.Use interval notation to represent the values of θ (betwen 0 and 2π) where tan(θ)>1.   Use interval notation to represent the values of θ (betwen 0 and 2π) where tan(θ)<−1.

Answer 1

ANSWERS

• tan(θ) > 1:, θ ,∈, {(π/4,, ,π/2) ∪ (5π/4, 3π/2)}

• tan(θ) < -1: ,θ ,∈, {(π/2, 3π/4) ∪ (3π/2, 7π/4)}

Step-by-step explanation

tan(θ) is a periodic function, that repeats its values between -π/2 and π/2.

When θ is close π/4, tan(θ) goes to infinity. The same happens for 5π/4, π/2 and 3π/2

Let's see the graph:

For θ between π/4 and π/2, the value of the tangent is more than 1. This is also true for θ between 5π/4 and 3π/2.

Then, when θ is between π/2 and 3π/4, and when it's between 3π/2 and 7π/4, tan(θ) is less htan -1.