Question

if A & B are second quadrant angles such that sinA=2/3 & cosB=-1/2, find
(a) sin(A+B)
(b) cos(A+B)
(c) tan(A+B)

Answer 1

ok what you need are the following numbers:
\(\cos(A)\) and \(\sin(B)\) so you can use the various formulas
do you know how to get them

Answer 2

uhh you would use pythagorean ?

Answer 3

for \(\sin(A)=\frac{2}{3}\) i would
for \(\cos(B)=\frac{1}{2}\) i would know instantly that \(\sin(B)=\frac{\sqrt{3}}{2}\)

Answer 4

\[\cos(A) = \frac{ \sqrt{5} }{ 3}\]

Answer 5

then i would use the equation\[\sin(u+v)=\sin u \cos v + \cos u \sin v\]

Answer 6

?

Answer 7

yes

Answer 8

wait... if angle B is a second quadrant angle, then shouldn't cos(B) = negative?

Answer 9

@Byteme good point !

Answer 10

oh ... sorry i meant it to be -1/2

Answer 11

oh ok good
still the same sine though
but \(\cos(A)=-\frac{\sqrt5}{3}\)

Answer 12

ye. so id substitute each to the sum & difference formulas?

Answer 13

yep...