What you're trying to find here is another angle with the same Sin, Cos value of whatever angle they want.

The short hand I learned was All students take calculus.

A is Quad I, everything is positive

S is Quad II, only Sin is positive, Cos is negative

T i s Quad III, sin and cos are both negative.

C is quad IV, Sin is negative Cos is positive.

for sin to be negative is has to be in quad III or IV. as maygyver noted that eliminates a, b, and d.

The reason why its C and not E is because of the reference angle that can be calculated.

For angles in Quad 1 the angle = its reference angle

quad 2 its 180-angle

quad 3 its angle - 180

quad 4 its 360 - angle

We are told that A is 200. that puts us in Quad III. So the reference angle would be 200 - 180 = 20.

The answer choices we have left puts us in the Quad 4. We already determined our reference angle. as 20.

So 360-X = 20. X would have to be 340.

sin 200 and sin 340 will both be -0.342

Sorry I know my explanation can be confusing so I'll try and simplify it below with an example

Cos 98 is - 0.139

Cos of what angle is also -0.139

98 degrees is in Quad 2. so to calculate the reference angle would be 180-98 = 82.

For Cos X to be a negative value it would have to be in Quad 3. We already have the reference angle so we just plug in the numbers and solve

So X - 180 = 82.

X = 262.

Try it out with a calculator and see what you get. You should get the same as Cos 98.