Question

find cos (alpha + Beta). sin alpha=5/13, alpha lies in Q1, and cos Beta=15/17 is also in Q1,


I already have B= +/- 12, and A=+/-8,
please help? :)

Answer 1

use sum identity for cosine
\[\cos(a+b) = \cos(a) \cos(b) - \sin(a) \sin(b)\]
so you need sin(b) and cos(a)
for that use pythagorean identity
\[\sin ^{2} \theta + \cos^{2} \theta = 1\]
\[(\frac{5}{13})^{2} + \cos^{2} a = 1\]
\[\cos a = \frac{12}{13}\]
do same thing to find sin(b)

Answer 2

I'm still pretty lost here :/

Answer 3

lets try triangle approach
you know that sin(a) = 5/13 and cos(b) = 15/17
draw 2 triangles reflecting those trig ratios

solve for the missing sides of the triangles to get the other trig ratios

does that make sense

Answer 4

agh, these just dont make sense to me, im sorry

Answer 5

but you said you already got 12 and 8 ... obviously you used pythagorean thm to get these numbers right?