Question

if tan = 5/12 and lies in quadrant 3 and cos -24/25 lies in quadrant 2 I'm confused how I begin to find sin (theta-beta)?

Answer 1

I'm assuming you meant to write

tan(theta) = 5/12 and cos(beta) = -24/25

Answer 2

Or do I have those backwards?

Answer 3

Yes sorry that's what I meant to write

Answer 4

ok so if tan(theta) = 5/12, and theta lies in quadrant 3, then what are sin(theta) and cos(theta) ?

Answer 5

sin and cos would be negative

Answer 6

that is correct, are you able to find their values?

Answer 7

No that's where I'm confused

Answer 8

when dealing with trig, you often either refer to the unit circle or a right triangle

Answer 9

in this case, it's easier to deal with a right triangle, so let's draw that out

Answer 10

then add in the angle theta

Answer 11

we are told that tan(theta) = 5/12

so what does that mean in terms of that right triangle I just drew (with the theta angle marker in there as well)?

Answer 12

tan is opposite over adjacent so opposite theta is 5 and underneath is 12

Answer 13

good, let's update the drawing with what you just told me



I also added in the labels for the sides. We don't know the hypotenuse yet, but we can find it. How?