Question

How do you find the exact value of tan 405 degrees?

Answer 1

`tan405=1`

Explanation:

On the unit circle, the nearest `x`-axis to `405` degrees is `360` degrees. This means the reference angle (difference between the two) is `45` degrees.

What do we know about `45` degrees?

The coordinates are `(sqrt2/2,sqrt2/2)`

where the `x` coordinate is the `cos` value and the `y` coordinate is the `sin` value. We understand `tantheta` to be defined as

`sintheta/costheta`

Thus, we have `(sqrt2/2)/(sqrt2/2)`, which simplifies to `1`.

We found `tan45`, which is the same as `tan405` because `45` degrees is its reference angle.

`tan405=1`

Hope this helps!