Question

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).

Answer 1

Answer:

$\frac{40}{41}$

Step-by-step explanation:

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

$\frac{9}{41}$

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:

${x}^{2} + {9}^{2} = {41}^{2}$

This implies that:

${x}^{2} = {41}^{2} - {9}^{2}$

${x}^{2} = 1600$

$x = \pm \sqrt{1600}$

$x = \pm40$

The cosine ratio is adjacent over hypotenuse.

$= \frac{ \pm40}{41}$

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

$= - \frac{40}{41}$