Question

Given that alpha is in quadrant II, beta is in quadrant III, sin(alpha)=3/4, and tan(beta)=4/3 find: a) cos(alpha+beta) b) sin(alpha-beta)

Answer 1

I would use the sum/difference formulas. \[\cos(\alpha+\beta)=\cos(\alpha)\cos(\beta)-\sin(\alpha)\sin(\beta)\]

Answer 2

ok

Answer 3

The other one is:
\[\sin(\alpha-\beta)=\sin(\alpha)\cos(\beta)-\sin(\beta)\cos(\alpha)\]

Answer 4

You also know that tan(beta)=4/3=sin(beta)/cos(beta)

Answer 5

That should be enough for this problem :)

Answer 6

oh ok. I didn't think about it that way, I use Tan=opposite/adjacent.

Answer 7

You could do and solve for beta :) Whichever way would be easier. I believe your way would after you know the sum/difference formulas I provided :P

Answer 8

how do I do it with alpha though?

Answer 9

use a^2+b^2=c^2?

Answer 10

and get the adjacent?

Answer 11

You can do that. Then you have all the ratios.

Answer 12

I tried that and got the wrong answer.

Answer 13

I got that the adjacent is -sqrt(7)

Answer 14

Negative?

Answer 15

yeah because its in the second quadrant...

Answer 16

Ahh, sorry. Yeah.

Answer 17

ok.

Answer 18

thanks.

Answer 19

no problem :P