Given sin A 35 and sin B 725 where A in in quadrant II and

Given sin A = 3/5 and sin B = 7/25 where A in in quadrant II and B is in quadrant I, use the sine of a sum or difference identity and cosine of a sum or difference identity to match each expression in column A with its exact value in column B.

Solution

Sin( A-B) = SinA CosB - CosASinB but A is in 2nd quandrant where Cos will be negative.

Therefore, Sin (A-B) = SinA CosB +CosA SinB

=3/5*24/25 + 4/5*7/25 = 4 / 5

Similalry, Cos (A-B) = -CosA CosB - SinA SinB

= -4/5*24*25 -3/5*7/25 = - 117/125