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

1 Answer
Jun 11, 2018

Answer:

#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!