Question

find sin (alpha+ beta), tan=21/20, alpha lies in quadrant 3, cos beta=(-8/17), b lies in q2

please give me details on how to do this, and what identity was used. thank you

Answer 1

Quadrant III

tan(x) > 0
sin(x) < 0
cos(x) < 0

tan(x) = sin(x)/cos(x)

sin(x+y) = sin(x)cos(y) + cos(x)sin(y)

That's about all you need. Go! Let's see what you get.

Answer 2

Oh, you may also need \(\sin^{2}(x) + \cos^{2}(x) = 1\)

Answer 3

I am still so confused :( where do I put the values for tan alpha and cos beta?

Answer 4

You just have to put in the time and think it through. All the pars are there.

\(\alpha\) is in III

tangent > 0 and we have \(\tan(\alpha) = 21/20\)
sine < 0
cosine < 0

\(\beta\) is in II

tangent < 0
sine > 0
cosine < 0 and we have \(\cos(\beta) = -8/17\)

\(\sin(\beta) = \sqrt{1 - (-8/17)^{2}}\)

\(\sin(\alpha)/\cos(\alpha) = \tan(\alpha) = 21/20\)
\(\sin^{2}(\alpha) + \cos^{2}(\alpha) = 1\)
Use these to find \(\sin(\alpha)\) and \(\cos(\alpha)\)