Corresponding Acute Angles Examples

What is sine of ?

Just how much is eleven-sixths of a pi?

Well, would be 2π, so we have less than that.

It would be hard to eat two pies by yourself, wouldn't it?

Wait, this means that our corresponding acute angle is . 2π is our angle on the closest x-axis.

The y value for is ½. That equals sin . Most excellent.

What is sine of ?

How should we approach this problem?

The same way we approach every problem, Pinky: try to take over the world!

Err, no. Maybe we should find the closest x-axis first.

equals 2π, which is only more than our angle. So 2π is the closest x-axis, with a corresponding acute angle of .

is in the fourth quadrant, between and 2π. (If graphing or working with radians isn't your thing, you could also check that it is between 270 and 360 degrees. The angle is 300 degrees, so it checks out that way as well.)

Sine of an angle equals the y-coordinate on the unit circle. The fourth quadrant has positive x and negative y. We're happy to be done with this problem, so we must be x ourselves.

What is the cosine of ?

We're spinning in circles from this problem.

Our angle isn't closest to π, or 2π, but to

If we move 2π along the unit circle, we end up exactly where we started. That means that will equal .

In another problem we already saw that the corresponding acute angle for is , and that it is in the second quadrant.