Find the Exact Value sin(pi/12)

Problem

sin(π/12)

Solution

1. Identify the angle as a difference of two common angles from the unit circle.

π/12=π/3−π/4

2. Apply the formula for the sine of a difference, which is sin(A−B)=sin(A)*cos(B)−cos(A)*sin(B)

sin(π/3−π/4)=sin(π/3)*cos(π/4)−cos(π/3)*sin(π/4)

3. Substitute the exact values for the sine and cosine of π/3 and π/4

sin(π/3)=√(,3)/2

cos(π/4)=√(,2)/2

cos(π/3)=1/2

sin(π/4)=√(,2)/2

4. Multiply the terms together.

√(,3)/2⋅√(,2)/2=√(,6)/4

1/2⋅√(,2)/2=√(,2)/4

5. Subtract the resulting fractions to find the final value.

√(,6)/4−√(,2)/4=(√(,6)−√(,2))/4

Final Answer

sin(π/12)=(√(,6)−√(,2))/4

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