given that cosA=3/5 and sinB=-15/17, with A in Q1 and B in Q4, use an appropriate sum formula to compute the exact value of cos(a+b)

Question

ganeshie8 · Answer

$\cos (A + B) = \cos (A) \cos (B) -  \sin (A) \sin (B)$

ganeshie8 · Answer

find watever u dont knw 
and plug them in above formula

anonymous · Answer

i realize that's the formula, but how do i find cos b and sin a?

ganeshie8 · Answer

use below identity :

$\sin^2\theta  +  \cos^2\theta  = 1$

ganeshie8 · Answer

you know 
cosA=3/5, 

can u find sinA ?

ganeshie8 · Answer

$\large  \sin^2A + \cos^2A = 1$

anonymous · Answer

gotcha

ganeshie8 · Answer

$\large  \sin^2A + (\frac{3}{5})^2 = 1$

anonymous · Answer

Think it just clicked.

ganeshie8 · Answer

solve $\sin A$

ganeshie8 · Answer

good :) but there is a trick,
u need to fix sign based on the quadrant

anonymous · Answer

so since it's cos if its quadrant 1 or 4 its positive, 2 or 3 its negative?

ganeshie8 · Answer

$\large  \sin^2A + (\frac{3}{5})^2 = 1 $

$\large  \sin^2A = 1 - \frac{9}{25} $

$\large  \sin^2A = \frac{16}{25} $

$\large  \sin A = \pm \frac{4}{5} $

ganeshie8 · Answer

since $A$ is first Quadrant,  "sin" is positive, so :

$\large  \sin A = + \frac{4}{5} $

anonymous · Answer

got it, thanks so much!

ganeshie8 · Answer

for cosB , you should take positive value ok
cuz B is in fourth Quadrant

ganeshie8 · Answer

:) u wlc !

anonymous · Answer

got cos(a+b)=84/85. Strangest answer...

ganeshie8 · Answer

http://www.wolframalpha.com/input/?i=%283%2F5%29%288%2F17%29+-+%284%2F5%29%28-15%2F17%29 looks correct !