Question

Is the function even or odd?

Answer 1

`f(\theta)=\cos(\theta)` is an even function.

Explanation:

Recall when it means when a function is even or odd. An even function has the following property:

`f(-x)=f(x)`

And an odd function has the following property:

`f(-x)=-f(x)`

So, let's test some values for cos(x).

Let's use π/3:

`f(\pi/3)=\cos(\pi/3)`

From the unit circle, was can see that this is 1/2 (refer to the x-coordinate).

Now, let's find -π/3. This is the same as 5π/3. Thus:

`f(-\pi/3)=\cos(-\pi/3)`

And again from the unit circle, we can see that this is 1/2.

Therefore, despite the negative, the function outputs the same value.

Cosine is an even function.

Notes:

Cosine is an even function and sine is an odd function. It's helpful to remember these as they can help you solve some trig problems!