Question

1. Find sin(a - b) if sin(a)= 5/13 where a is in the second quadrant and cos(b)= -7/25 where b is in the third quadrant.

2. Find cos(a + b) if sin(a)= 8/17 where a is in the first quadrant and tan(b)= -7/24 where b is in the second quadrant.

Please explain. Thank you!

Answer 1

This is what I got for number 1:

sinα = 5/13
cos²α = 1-sin²α = 144/169
Since α is in the second quadrant, cosα = -√(144/169) = -12/13.

cosβ = -7/25
sin²β = 1-cos²β = 576/625
Since β is in the third quadrant, sinβ = -√(576/625) = -24/25

I just do not know how to do the sum formula for sine?

...and I am not sure how to do number 2?

Answer 2

Are you not aware of the formula?

Answer 3

\[\large\rm sin(a-b) = sina* cosb - cos a *sinb \]\[\large\rm cos(a-b) = cosa* cosb + sin a *sinb \]

Answer 4

@FaiqRaees so like this sin(-12/13) * cos(-24/25) - cos(-24/25) * sin(-12/13)?

Answer 5

why have you changed the angle values?

Answer 6

What are the angle values?

Answer 7

sin(a)= 5/13 cos(b)= -7/25

Answer 8

Oh I see let me redo it then...

Answer 9

So like this sin(5/13) * cos(-7/25) - cos(5/13) * sin(-7/25)?

Answer 10

http://www.wolframalpha.com/input/?i=sin(5%2F13)+*+cos(-7%2F25)+-+cos(5%2F13)+*+sin(-7%2F25)

Answer 11

I do not see that as a choice?

Answer 12

That is the way of the formula?

Answer 13

http://www.wolframalpha.com/input/?i=5%2F13+*-7%2F25+-+(5%2F13+*+-7%2F25)

Answer 14

Oh I see they havent given you values for sin b and cos a. So you have to find them out first

Answer 15

and then plug them in the equation

Answer 16

Can you do it?