still not getting it

Question

You are given that sin(A)=−7/25, with A in Quadrant IV, and sin(B)=−12/13, with B in Quadrant III. Find cos(A+B). Give your answer as a fraction.

Answer 1

cos(A+B)=cos(A)cos(B)-sin(A)sin(B). Use the given information to determine cos(A) and cos(B) using the Pythagorean Identity, cos²x=1-sin²x, and the designated sign based on the quadrant given. Once you have the values (fractions) for cos(A) and cos(B). Calculate cos(A+B).

Answer 2

Hi Dylan, can you use the Sum Formula? It says that cos(A+B) = cosA cosB - sinA sinB

If sinA = -7/25 in Quadrant 4, that means that cosA = + 24/25 (pythag thm with hypotenuse = 1)

If sinB = -12/13 in Quadrant 3, that means that cosB = - 5/13 (need to adjust sign depending on quadrant)

Now we just plug into the Sum Formula:

cos(A+B) = (24/25) (-5/13) - (-7/25)(-12/13) = (-120/325) - (84/325) = -204/325