cos theta = -sqrt2/3 , where pi is less than or equal to theta which is less than or equal to 3pi/2
tan beta = 4/3 , where 0 is less than or equal to beta which is less than or equal to pi/2
what is the exact value of sin ( theta + beta ) ?
final answer must be in a simplified fraction
Let A be the first "theta"
A is in the 3Q ......so the sine is negative and is given by -√ [ 3^2 - (√2)^2] / 3 =
- √7 / 3
Let B be the second "theta"
B is in the 1Q and r = 5
sin B = 4/5 cos B = 3/5
sin ( A + B) = sin A cos B + sin Bcos A =
(-√7/3) ( 3/5) + (4/5) ( -√2/3) =
[ -3√7 - 4√2 ] / 15