Question

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

Answer 1

To solve this problem, you'll need to use some trigonometric identities.
An easy way to remember the angle sum formulas is to remember that
sin has sin AND cos (different), therefore the sign is the same
\[\sin(a+b) = \sin(a)\cos(b) + \sin(b)\cos(a)\]
cos has sin or cos (same), therefore the sign is the opposite
\[\cos(a+b) = \cos(a)\cos(b) - \sin(a)\sin(b)\]

Answer 2

How would cos(B)=sqrt5/3? Thats all I dont understand

Answer 3

Which part of the question are you talking about? I think the problem states that cosB=-1/2?

Answer 4

But to solve the answer wouldn't cos(B) = sqrt5/3?

Answer 5

cos(A)* sorry

Answer 6

Yes, cos(A) = sqrt5/3 based on the Pythagorean theorem.

Answer 7

Ohhhhhh alright, thank you!!! Would that also be the same for sinB=sqrt/2?

Answer 8

yes, I think you just forgot to type the 3 in the sqrt(3)/2

Answer 9

Sorry!! I meant sqrt3/2!

Answer 10

Thank you so much!