Find the Exact Value sin(pi/3-pi/4)

Problem

sin(π/3−π/4)

Solution

1. Identify the appropriate trigonometric identity for the sine of a difference, which is sin(A−B)=sin(A)*cos(B)−cos(A)*sin(B)

2. Assign the values A=π/3 and B=π/4 to the identity.

3. Substitute the known exact values for the trigonometric functions of these special angles: sin(π/3)=√(,3)/2 cos(π/3)=1/2 sin(π/4)=√(,2)/2 and cos(π/4)=√(,2)/2

4. Multiply the terms: (√(,3)/2)*(√(,2)/2)=√(,6)/4 and (1/2)*(√(,2)/2)=√(,2)/4

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

Final Answer

sin(π/3−π/4)=(√(,6)−√(,2))/4

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