Question

True or FalseThe only even trigonometric function are the cosine and secant functions.

Short answer

The statement "The only even trigonometric function are the cosine and secant functions" is true.

Step-by-step solution

Step 1. Given information.

We have:

The only even trigonometric function are the cosine and secant functions.

Step 2. Find whether the statement is true or false.

Even function: A function is even if $f\left(-x\right)=f\left(x\right)$for all $x\in \mathrm{ℝ}$.

Substitute $\theta =-\theta$:

$$\begin{gathered} \cos \left(-\theta \right)=\cos \theta \\ sec(-\theta )=sec\theta \end{gathered}$$

Hence, cosine and secant are even functions.