Help !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Question

Use addition formulas and the values of sinθ and cosθ for θ=π/4, π/3 to compute sin7/12π and cos7/12π exactly.

(Use symbolic notation and fractions where needed.)

sin7/12π=

cos7/12π=

 

Answer 1

The trick is 7/12 = 3/12 + 4/12 = 1/4 + 1/3.

So use the addition formulas for sine and cosine to get the results.

sin(π/4 + π/3) = sin(π/4)cos(π/3)+sin(π/3)cos(π/4)

cos(π/4 + π/3) = cos(π/4)cos(π/3)-sin(π/3)sin(π/4)

You can use the unit circle to get the sine and cosine values and just do the arithmetic.