Question

Find the exact value of the trigonometric expression given that
sin u = 5/13 and cos v =− 3/5
(Both u and v are in Quadrant II.)
tan(u + v)

Answer 1

Knowing that u and v are in Quadrant II, where does that put u + v? It's always good to know before we start looking for things.

Answer 2

I understand that part )

Answer 3

Tan is negative

Answer 4

It is of great value to TELL us where you are so we don't have to guess.

Are you sure?

\(\pi/2 < u < \pi\)

\(\pi/2 < v < \pi\)

\(\pi < u +v < 2\pi\) - From this, it could go either way.

What's your plan? Calculate the two tangents and use the tangent of a sum formula or use the sine and cosine sum functions and calculate that tangent?

Answer 5

Is it \[\frac{ (-5/12) +(4/-3) }{ 1-(-5/12)(4/-3) }\] Is this right so far?

Answer 6

So, you are calculating the two individual tangents. How did you do that?

Answer 7

I found it through reference triangles and SOH CAH TOA

Answer 8

@3mar Can you check my work so far?

Answer 9

-5/12 = tan(u) -- That's good.

Answer 10

-4/3 = tan(v) -- That's good.

Answer 11

Your arithmetic looks fine.

Answer 12

I got 63/16 for my final answer and it is wrong! I am so worried now because this homework is due before 12:00. Please tell me where I went wrong

Answer 13

I thought you said it was negative?

Answer 14

I guess I mistyped! Thank you!!!

Answer 15

Sorry I will be back within 45 min
Salam!

Answer 16

@3mar I got it now! Thanks though!)

Answer 17

Ok.
That is good!