Sign and Size

Every exact value comes from two questions. Size: the reference angle names the special triangle under the point, and that gives the value without its sign. Sign: the quadrant.

Take $\cos\left(135^{\circ}\right)$. 135° is in quadrant II with reference angle 45°, so the size is $\cos\left(45^{\circ}\right)$, √2/2, and the cosine is negative in quadrant II: $\cos\left(135^{\circ}\right) = -\cos\left(45^{\circ}\right)$, which is −√2/2.

On the board the chip Use the reference angle 45° turns cos 135° into −cos 45°, sign included, and the note under the line names the quadrant. Then work out the value at the reference angle. In this lesson the board will not turn cos 135° into a value in one press.