Please help me with the following question Show me all steps

Please help me with the following question! Show me all steps! thank you!!!

32. and sin = and the erminal side of a lies in quadrant 1 and the terminal side Find the exact value of sin( + ) if sindr = of lies in quadrait ll.

Solution

32 . sin ( @ + B ) = ?

sin @ = -3/5 @ -> 3rd quadrant

cos @ = +- ( 1 - sin²@)^1/2

= + - ( 1 - ( -3/5)²) ^1/2

= - 4/5 [ cos @ = -ve in 3rd quadrant]

sin B = 1/5

cos B = + - ( 1- sin²B )^1/2

= + - ( 1 - 1/25)^1/2

= - ( 24)^1/2 / 25 [ cos B = -ve in 2nd quadrant]

sin ( @ + B) = sin @ * cos B + cos @ * sin B

= ( -3/5) * ( - 24^1/2 /5) + ( - 4/5)* ( 1/5)

=[ 3*( 24)^1/2 / 2]5 - [4/25]

= 0.427