SOLUTION: Use an Addition or Subtraction Formula to find the exact value of the expression, as demonstrated in Example 1. 1. tan(-11pi/12) 2. sin(-11pi/12)

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Question 761565: Use an Addition or Subtraction Formula to find the exact value of the expression, as demonstrated in Example 1.
1. tan(-11pi/12)
2. sin(-11pi/12)


Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
Use an Addition or Subtraction Formula to find the exact value of the expression, as demonstrated in Example 1.
1. tan(-11pi/12)=tan(13π/12)=tan(9π/12+4π/12)=tan(3π/4+π/3)=-1+√3)/1-tan(3π/4)*tan(π/3)
=(-1+√3)/(1-(-1*√3)=-(1-√3)/(1+√3)*(1+√3)/(1+√3)=(1-2√3+3)/(1-3)=(4-2√3)/2=2-√3
calculator check:
tan(-11π/12≈0.2679
exact value=2-√3≈.2679
..
2. sin(-11pi/12)=sin(13π/12)=sin(9π/12+4π/12)=sin(3π/4+π/3)=√2/2*1/2+(-√2/2*√3/2
=√2/4-√6/4=(√2-√6)/4
Calculator check:
sin(-11π/12)≈-0.2588
Exact value=(√2-√6)/4≈0.2588