How do you solve this without using a calculator

Answer:
A
Explanation:
You must know the basics of Trigonometry to solve this.
First, you must know that
[tex] \frac{3\pi}{4} [/tex]
lies in the second quadrant, so sin is negative.
Next, since
pi/4, is the reference angle of 3 pi/4, this means that we can set up a right triangle with pi/4 as an angle, we get
[tex] \cos( \frac{3\pi}{4} ) = \frac{ \sqrt{2} }{2} [/tex]
[tex] \sin( \frac{\pi}{4} ) = - \frac{ \sqrt{2} }{2} [/tex]
So the answer is A