When drawn in standard position, an angle a has a terminal ray that lies in the second quadrant and whose sine is equal to 9/41. Find the cosine of a in rational form (as a fraction).

Step-by-step explanation:

We have the angle in standard post has a sine ratio of

This means the opposite side length of the corresponding right triangle is 9 units and the hypotenuse is 41 units.

Using Pythagoras Theorem, the adjacent side length can be found using:

This implies that:

The cosine ratio is adjacent over hypotenuse.

Since we are in the second quadrant, the cosine ratio is negative;

except a rational number. : )