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)

Question

anonymous · Answer

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

anonymous · Answer

ok

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

That should be enough for this problem :)

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

how do I do it with alpha though?

anonymous · Answer

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

anonymous · Answer

and get the adjacent?

anonymous · Answer

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

anonymous · Answer

I tried that and got the wrong answer.

anonymous · Answer

I got that the adjacent is -sqrt(7)

anonymous · Answer

Negative?

anonymous · Answer

yeah because its in the second quadrant...

anonymous · Answer

Ahh, sorry. Yeah.

anonymous · Answer

ok.

anonymous · Answer

thanks.

anonymous · Answer

no problem :P