Find the indicated trig function of
θ, if θ is an angle in standard position with the terminal side defined by the given
point.
(12, 16); Find cos θ.
answer is 4 over 5 but how do i find this?
please help :P
(12, 16) means that the x-coordinate is 12 and the y-coordinate is 16. the x-coordinate gives the horizontal distance while the y gives the vertical distance. this means we form a right-triangle with an acute angle $\displaystyle \theta$ at the origin that has a base length of 12 and a height of 16 (draw a diagram). now all we need to find is the hypotenuse (since cosine = (adjacent)/(hypotenuse)).
use Pythagoras' theorem to find the hypotenuse (or you could notice this is a 3-4-5 triangle). once you do that just plug in the values into the equation:
$\displaystyle \cos \theta = \frac {\mbox{Adjacent}}{\mbox{Hypotenuse}}$
here, the adjacent side is 12 (you can see that from the diagram)