Question

Determine the value(s) of θ (between 0 and 2π) where tan(θ)=1.θ=Determine the value(s) of θ (between 0 and 2π) where tan(θ)=−1.θ=

Answer 1

The angles where the tangent function equals 1 are 45 degrees and 225 degrees. The angles where the tangent function equals -1 are 135 degrees and 315 degrees.

Step-by-step explanation:

To determine the value(s) of θ (between 0 and 2π) where tan(θ) = 1, we need to find the angles where the tangent function equals 1.

The tangent function is equal to the ratio of the opposite side to the adjacent side in a right triangle. In the first quadrant, where the values of sine and cosine are positive, the angle whose tangent is 1 is π/4 or 45 degrees.

In the third quadrant, where the values of sine and cosine are negative, the angle whose tangent is 1 is 5π/4 or 225 degrees.

To determine the value(s) of θ (between 0 and 2π) where tan(θ) = -1, we need to find the angles where the tangent function equals -1. In the second quadrant, where the sine is positive and the cosine is negative, the angle whose tangent is -1 is 3π/4 or 135 degrees.

In the fourth quadrant, where the sine is negative and the cosine is positive, the angle whose tangent is -1 is 7π/4 or 315 degrees.