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

1 Answer
Jacobi J.
Jun 11, 2018

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!

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