Question

Please help!
angle A in Quadrant II, tanA=-12/5
angle B in Quadrant III, sinB=-3/5

sin ( A + B) =
a. 33/65
b. -33/65
c. -63/65
d. 63/65

Answer 1

@IloveCharlie what's the sign of sin and cos in quadrant ii and iii ?

Answer 2

I'm not sure :/ It's not part of the problem...

Answer 3

ok, I'll tell you
sin= +ve and cos =-ve in II quadrant
sin=-ve and cos=-ve in III quadrant

Answer 4

What is ve?

Answer 5

Well, do you know the equation for the sum of angles for sine?

Answer 6

No

Answer 7

Sin (A + B) = sin A cos B + sin B cos A

Answer 8

The only thing that you can substitute into that equation at this point is that sin B = -3/5. The rest you'll have to extrapolate.

Answer 9

Do you know your basic trig ratios, like sine is opposite/hypotenuse, cosine is adjacent/hypotenuse, etc.?

Answer 10

You know that tan A = -12/5. Tangent is opposite/adjacent. What would sine A and cosine A be then?

Answer 11

Ignore the negative in front of the 12, for now.

Answer 12

Sine: 12/13 cosine: 5/13 ?

Answer 13

Yup, good =)

Now is when the signs come into play. That's what ash was talking about. There is a phrase called "All Students Take Calculus" that tells you what trig function is positive/negative in what quadrant.
All - all trig functions positive in Q1
Students - Sine positive in Q2, rest negative
Take - Tangent positive in Q3, rest negative
Calculus - Cosine positive in Q4, rest negative

So based on that, can you tell me sin A and cos A again?

Answer 14

... Hmm. So Q2: 12/13, -5/13 and Q3: -12/13, -5/13

Answer 15

@Rogue ?

Answer 16

Correct for Q2, but you have to use a different triangle for angle B. You know that sin B = -3/5, so can you set up the triangle?

Answer 17

So what is Cos B?