Question

let theta be an angle in quadrant 4 such that sin theta=-2/5
find the exact values of sec theta and tan theta
PLEASE HELP!!!

Answer 1

So I've drawn a triangle in quadrant 4.

Answer 2

Rememeber your side relations for the sine function?

Answer 3

Opposite over hypotenuse

Answer 4

Ok good.
Here is a tip for labeling your sides.
`The hypotenuse should always be positive`.
So we'll choose to pair the negative sign with the numerator.

Answer 5

We can use the Pythagorean Theorem to find our missing side.

\[\Large\rm a^2+(-2)^2=5^2\]\[\Large\rm a=?\]

Answer 6

so a^2=21...a=4.58

Answer 7

\[\Large\rm a=\sqrt{21}\]Ok good. Let's leave it like this.