1 Find the exact value of each expression sin 7pi6 13pi3 2

1. Find the exact value of each expression. sin (7pi/6 - 13pi/3)

2. Find the exact values of the sine, cosine, and tangent of the angle. 7/12 = /3 + /4

Sin(7/12)=

Cos(7/12)=

Tan(7/12)=

3. Write the expression as the sine, cosine, or tangent of an angle. cos (/7) cos (2 /5) sin( /7) sin (2/5)

sin (7pi/6 - 13pi/3)

= sin(pi +pi/6 - ( 4pi +p/3))

Use sin(A -B) = sinAcosB - cosAsinB

So, sin (7pi/6 - 13pi/3) = sin7pi/6cos13pi/3 - sin13pi/3cos7pi/6

= sin(pi +pi/6)cos(4pi +pi/3) - sin(4pi +pi/3)cos(pi +pi/6)

= -sinpi/6cospi/3 + sinpi/3cospi/6

= -(1/2)(1/2) + (sqrt3/2)(sqrt3/2)

= -1/4 + 3/4

= 2/4

= 1/2