Posted by **tony** on Sunday, June 16, 2013 at 11:20pm.

Find cos(A+B).

cos A=1/3 and sin B=-1/2, with A in quadrant I and B in quadrant IV.

- trig -
**Bosnian**, Monday, June 17, 2013 at 12:42am
cos A = 1 / 3

sin A = + OR - sqrt ( 1 - cos A ^ 2 )

sin A = + OR - sqrt ( 1 - ( 1 / 3 ) ^ 2 )

sin A = + OR - sqrt ( 1 - 1 / 9 )

sin A = + OR - sqrt ( 9 / 9 - 1 / 9 )

sin A = + OR - sqrt ( 8 / 9 )

sin A = + OR - sqrt ( 4 * 2 / 9 )

sin A = + OR - sqrt ( 4 ) * sqrt ( 2 ) / sqrt ( 9 )

sin A = + OR - 2 * sqrt ( 2 ) / 3

sin A = + OR - ( 2 / 3 ) * sqrt ( 2 )

In quadrant I sine are positive so :

sin A = ( 2 / 3 ) * sqrt ( 2 )

sin B = - 1 / 2

sin B = + OR - sqrt ( 1- cos B ^ 2 )

cos B = + OR - sqrt ( 1 - ( - 1 / 2 ) ^ 2 )

cos B = + OR - sqrt ( 1 - 1 / 4 )

cos B = + OR - sqrt ( 4 / 4 - 1 / 4 )

cos B = + OR - sqrt ( 3 / 4 )

cos B = + OR - sqrt ( 3 ) / 2

In quadrant IV cosine are positive so :

cos B = sqrt ( 3 ) / 2

cos ( A + B ) = cos A * cos B - sin A * sin B

cos ( A + B ) = ( 1 / 3 ) * sqrt ( 3 ) / 2 - ( 2 / 3 ) * sqrt ( 2 ) * ( - 1 / 2 )

cos ( A + B ) = ( 1 / 6 )sqrt ( 3 ) + ( 2 / 6 ) * sqrt ( 2 )

cos ( A + B ) = ( 1 / 6 ) [ sqrt ( 3 ) + 2 sqrt ( 2 ) ]

cos ( A + B ) = [ sqrt ( 3 ) + 2 sqrt ( 2 ) ] / 6

- trig -
**Steve**, Monday, June 17, 2013 at 4:30am
what's all this work?

A is in QI, so sinA = √8/3

B is in QIV so cosB = √3/2

and then as done in the final paragraph

## Answer this Question

## Related Questions

- trig - can someone please help me with this problem. i'm doing my review right ...
- mth, trig - Given cos a=-7/25 in quadrant II , and sin b=-12/13, in quadrant IV...
- Trig - Find cos(s+t) if cos s= -1/2 and sin t= 3/5, s and t are in quadrant II. ...
- TRIG! - Posted by hayden on Monday, February 23, 2009 at 4:05pm. sin^6 x + cos^6...
- Trig - find sin(s+t), given that sin t=1/3, t in quadrant 2, and cos s = -2/5, s...
- trig - Find cos(a=b). sin a = 3/5, a lies in Quadrant II, and cos b = 5/13, b ...
- trig - if sin a=4/5 and is quadrant 2 and sin b= 8/17 and is in quadrant 1, find...
- trig - how do you work find sin (a-B)beta sign. sin a = 12/13,a lies in quadrant...
- Alg2/Trig - Find the exact value of the trigonometric function given that sin u...
- trig - suppose sin(x)=4/5 and cos(y)=-12/13, and x and y are in the second ...