00:01
Okay, so we're asked to find the exact value of tangent of 40 degrees plus tangent of 140 degrees.
00:06
And we can use reference angles to solve this problem.
00:09
Now, the reference angle of 40 degrees would simply be 40 degrees because it's less than 90 degrees.
00:15
But the reference of 140 degrees would be different.
00:19
So we have zero there, 90 degrees there, 180 degrees there, 270 degrees here, and a full circle would make 360 degrees here.
00:33
So tangent 140 degrees would be somewhere in the second quadrant.
00:38
So that angle right there is 140 degrees.
00:42
And the reference angle we're trying to find is that angle right there.
00:46
If an angle is in the second quadrant, the reference angle can simply be found from subtracting from 180 degrees, and we would get 40 degrees.
00:59
But that's not the final answer...