find the exact value

Question

Use a sum or difference formula to find the exact value of the following. sin (7pi )/(30) cos (7pi )/(60)+ cos(7pi )/(30) sin (pi )/(60)

Answer 1

The sum formula to use is:

sin(x + y) = sin x cos y + cos x sin y

sin (7 pi/30 + 7pi/60)

Use the LCD of 60 to combine the two fractions.

sin (14 pi/60 + 7pi/60)

sin (21 pi/60)

reduce the fraction

sin (7 pi/20)

The last step is to find the sin value of the angle (7pi/20).