Question

how do i do this step by step ?

Answer 1

: cos(a - b) = cos(a).cos(b) + sin(a).sin(b) <=== do i use this to start off

Answer 2

Yes, good start point.

Answer 3

Remember to use the usual formulas when you don't know the value of the cos or sin\[sinx=\pm\sqrt{1-\cos^2x}\]. And select the appropiate sign using the quadrant.

Answer 4

so it's just cos(4/5+(-12/13))

Answer 5

and then 16/65?

Answer 6

No, you must use the last formula you wrote.\[\cos(\alpha+\beta)=\cos\alpha\cos\beta-\sin\alpha\sin\beta\]

Answer 7

You need cos\alpha and sin\beta first. Have you found them

Answer 8

i thought it was already given in the problem as A being 4/5 and B being -12/13

Answer 9

Not exactly, the problem says\[\sin\alpha=4/5\]

Answer 10

You can find \[\cos\alpha=\sqrt{1-(4/5)^2}=3/5\]

Answer 11

Also, the problem says\[\cos\beta=-12/13\] so\[\sin\beta=\sqrt{1-(12/13)^2}=5/13\]

Answer 12

Now, you can find the result using the formula,\[\cos(\alpha+\beta)=3/5\cdot(-12/13)-4/5\cdot5/13\]

Answer 13

oh so your saying i still needed to be find sin B and Cos A ... oh ok that makes sense

Answer 14

Yes, exactly. As they are in the first quadrant and the second, you need the positive sign, as I choosed before.