Thread: coterminal

Express tan 245° as a function of an angle in Quadrant I.

Honestly I'm not even sure how I could express a value as a function... must've slept through this one?

Help appreciated!

The "function" here is trigonometric function.
Like sine, cosine, tangent, etc.

The values of these functions, as shown by your calculator, are expressed as the functions of acute angles, or of angles in the 1st Quadrant, only.
All angles in the 1st quadrant, except 0 and 90 degrees, are acute angles.

So the given angle is more than 90 degrees (or pi/2 radians), find its equivalent acute angle from the x-axis.

245 degrees is more than 90 degrees.
245 degrees is in the 3rd quadrant.
The angles along the x-axis are 0 and 180 degrees .
So the equivalent acute angle of 245deg is 245 -180 = 65 deg.

Hence,
tan(245)
= tan(65) -------------answer.

Now, it just happens that tangent is positive in both the 1st and 3rd quadrants. Otherwise, be careful with the sign of the equivalent function of an angle in the 1st quadrant.
Like, tangent is negative in the 2nd and 4th quarants.

Oh wow, I really need to get some rest, I was over-thinking it...

Thanks a ton!