Question

Find cos θ if sin θ = -12/13 and tan θ > 0.

A.-5/12
B.-5/13
C.12/5
D.-13/12

Answer 1

If tangent is positive and sin is negative, what quadrant are you in?

Answer 2

3rd?

Answer 3

Tangent is sin / cos. It can only be positive if both sin and cos are positive or both sin and cos are negative.

Answer 4

@Mertsj ok. and how do i apply that to the problem.

Answer 5

cosine is like x. sine is like y. In what quadrant are both sin and cosine positive?

Answer 6

@Mertsj first quadrant.

Answer 7

yes. And in what quadrant are both sin and cos negative?

Answer 8

Or in other words...in what quadrant are both x and y negative?

Answer 9

@Mertsj third quadrent.

Answer 10

So, since the tangent is positive, our angle must be in either the first or the third quadrant.

Answer 11

But the problem tells that the sin (which is like y) is negative. So which quadrant is it in? I or III ????

Answer 12

the third @Mertsj

Answer 13

quadrent sorry i just take a while to think

Answer 14

Now...draw a picture of an angle in quadrant III whose sin is 12/13 and then use the Pythagorean Theorem to find the missing side.

Answer 15

alright i got A as an answer. but im not sure if its right. @Mertsj

Answer 16

What did you get?

Answer 17

No. A is not correct.

Answer 18

The definition of cosine is side adjacent over hypotenuse.

Answer 19

so 12/5 would be the answer if its adjacent over hypotenuse. is that correct @Mertsj

Answer 20

What did you get for the missing side?

Answer 21

1.173 @Mertsj

Answer 22

Do you know the Pythagorean Theorem?

Answer 23

isnt it square all and divide by hypotenuse ( longest side)? @Mertsj