If cos 0305 and cos 0738 with both angles terminal rays in

If cos = 0.305 and cos = 0.738 with both angles’ terminal rays in Quadrant-I, find the values of

a) sin(+)=

b) sin()=

If cos = 0.757 and cos = 0.978 with both angles’ terminal rays in Quadrant-I, find the values of

(a) cos(+)=

(b) sin(+)=

show your work please (:

Solution

a) and b) cos = 0.305 ========> sin = 0.952

cos = 0.738 =========> sin = 0.675

sin( + ) = sin()cos() + cos()sin() = 0.952* 0.738 + 0.305 *0.675 = 0.9085

sin( – ) = sin()cos() – cos()sin() = 0.952* 0.738 - 0.305 *0.675 = 0.4967

c) and d) cos = 0.757 ========> sin = 0.653

cos = 0.978 =========> sin = 0.209

cos( + ) = cos()cos() – sin()sin() = 0.757*0.978 - 0.653*0.209 = 0.604

sin( + ) = sin()cos() + cos()sin() =0.653* 0.978 + 0.757 *0.209 = 0.797