Question

How do you find cos if $sin=5/13$ ?

Answer 1

Given $sinx=\frac{5}{13}$
$\therefore \frac{\text{opposite side}}{\text{hypotenuse}}=\frac{5}{13}$

By Pythagorean Theorem
If opposite side = $5$ units and hypotenuse = $13$ units
then adjacent side = $12$ units
We know that $cosx=\frac{\text{adjacent side}}{\text{hypotenuse}}=\frac{12}{13}$
However, we need to note that if the angle is in Quadrant II then the adjacent side will actually be a negative value,
so
$cosx=\frac{12}{13}$ for an angle in Q|
or
$cosx=-\frac{12}{13}$ for an angle in Q ||
(the angle can't be in Q III or Q IV, since $sin>0$)