Question

How do you evaluate `sec (4pi)`?

Answer 1

`sec(4pi)=1`

Explanation:

Use the reciprocal identity:

`sectheta=1/costheta`

Also, since all the trigonometric functions are periodic, you can subtract or add any multiples of `2pi` until the angle is a bit easier to calculate:

`color(white)=sec(4pi)`

`=1/cos(4pi)`

`=1/cos(4picolor(red)-color(red)(2pi))`

`=1/cos(2pi)`

`=1/cos(2picolor(red)-color(red)(2pi))`

`=1/cos(0)`

Here's a unit circle to remind us of some trig values for cosine:

Now we can see that `cos(0)` is `1`, so:

`color(white)=1/cos(0)`

`=1/1`

`=1`

That's the result. We can check our work using a calculator:

![https://www.desmos.com/calculator]()