Question

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

Answer 1

Good morning! At least it's still morning here in Southern California.

If sin theta is -12/13, in which two quadrants could theta NOT lie?

That means that theta must either be in quadrant ( ) or quadrant ( ).

Answer 2

quadrant 2 and 3?

Answer 3

Please explain your reasoning.

Answer 4

am i right though?

Answer 5

About Q2: no. Q3: yes. Why?

Answer 6

cause in quadrant three only tangent is positive

Answer 7

True. But how do you define the sine function?

Answer 8

uh sine is opposite/ hypotenuse

Answer 9

Right, and in which quadrants is the "opposite side" negative?

Answer 10

quadrant 4?

Answer 11

Yes, and is that the only quadrant in which the opp side is negative?

Answer 12

and quadrant three

Answer 13

Yes. This business of identifying which quadrants apply to positive and negative opposite sides and positve and negative adjacent sides is truly important.

In which quadrants is the cosine of x negative, and why?

Answer 14

quadrants 2 and three right?

Answer 15

Right. And why?

Answer 16

because in quadrant 2 only sine is positive and in quadrant 3 only tangent is positive

Answer 17

I'd rather that you remember cos theta = adj side over hypotenuse and that the adj side is negative in QII and QIII.

Again, this know-how is important and it is worth your time to review and practice this.

Answer 18

You've posted: "Find cos θ if sin θ = (-12/13) and tan θ > 0."

Based on our recent discussion, theta must be in which quadrants?

Answer 19

quadrant three and four

Answer 20

That's right.
OK. Supposing that we focus on the theta (angle) that is in Q4.
Please determine the length of the adjacent side. How would you do that?
You might want to sketch this angle for yourself and identify opp and adj sides as well as hyp.

Answer 21

In Q4, the opp side is -12, the hyp is 13, and the adj side is ???

Answer 22

5

Answer 23

so the answer would be 5/-12

Answer 24

Good. Now, how do we define the cosine function?

cos theta = ???

Answer 25

adjacent/ hypotenuse

Answer 26

In Q4, the adj side has length ??
and the hypotenuse has length ??
and therefore the cosine of theta in Q4 is ??

Answer 27

5 and -12 so therefore the cosine of theta is 5/-12

Answer 28

Let's backtrack a moment. Is the adj side pos or neg in Q4? Is the hyp pos or neg there?

Answer 29

"5 and -12 so therefore the cosine of theta is 5/-12"
To save your time: the hyp is never negative. Only the adj and the opp can be neg.
So, please modify the above statement from you.

Answer 30

so the cosine of theta is 12/5??

Answer 31

Is that adj over hyp or hyp over adj? Which of these is correct?

Answer 32

Sorry this has turned out to be such a lengthy process. But this review is important. Are you able to give this discussion your full attention right now, or would you prefer to resume it later? I'd like to keep a steady stream of messages going back and forth if at all possible.

Answer 33

its just that I'm finishing an assignment that is being timed and I'm just answering the other questions

Answer 34

Only you can decide how you want to use your time, but remember, every minute spent away from our discussion means a minute in which I have to find something else to do; this is not efficient for me.

Answer 35

Of course I could move through this problem quickly, giving you answers, but that'd be pointless if y ou don't have enough of the required background knowledge to answer future similar questions.

Answer 36

Because the adj side is + in Q4, and because the hypotenuse is always +, the cosine of theta in Q4 is therefore what? Before you answer, please type the formula for the cosine of theta.

Answer 37

cosine is adjacent/ hypotenuse

Answer 38

yes, so in this case, the cosine of theta is what?

Answer 39

12/5

Answer 40

but isn't that hyp over adj?

Answer 41

yes so its 5/12 my bad

Answer 42

I'd suggest you make up some flash cards or a review sheet and refer to it often until you can confidently identify which quadrants contains a given angle, as well as the def'ns of the 6 trig functions.
Now

Answer 43

you have one sub-problem left: you are to determine the cosine of theta in Q3, if I remember correctly.
In Q3 what sign does the adj have?

Answer 44

in Q3, what sign does the hyp have?
the opp side?
What is the cosine of theta in Q3?

Answer 45

I need to ask you again: are you able to give this discussion your full attention, respecting the time I am giving to you voluntarily, or would you prefer to complete your online test instead?

Answer 46

I'm sincerely glad we could work together. Hope there is a next time when you're not distracted by other tasks. Best of luck to you. Bye.