Question

Find the exact values of cos 3 pi/4 radians sin 3 pi/4 radians.

Answer 1

If you consult the unit circle, you will see that:

$cos(\frac{3\pi}{4}) = -\frac{\sqrt{2}}{2}\\\\sin(\frac{3\pi}{4}) = \frac{\sqrt{2}}{2}$

3pi/4 in degrees is 3pi/4 * 180/pi = 3/4 * 180 = 135 degrees. And please refer to the attachment to how you can obtain the values above.

Now, lets multiply it together.

$-\frac{\sqrt{2}}{2} \cdot \frac{\sqrt{2}}{2} =\\\\-\frac{2}{4} =\\\\ \boxed{\bf{-\frac{1}{2}}}$

So, cos(3pi/4)sin(3pi/4) = -1/2