Find the Exact Value cos((3pi)/4-pi/6)

Problem

cos((3*π)/4−π/6)

Solution

1. Identify the appropriate trigonometric identity for the cosine of a difference, which is cos(α−β)=cos(α)*cos(β)+sin(α)*sin(β)

2. Substitute the values α=(3*π)/4 and β=π/6 into the identity.

cos((3*π)/4−π/6)=cos((3*π)/4)*cos(π/6)+sin((3*π)/4)*sin(π/6)

3. Determine the exact values for the trigonometric functions at the given angles using the unit circle.

cos((3*π)/4)=−√(,2)/2

cos(π/6)=√(,3)/2

sin((3*π)/4)=√(,2)/2

sin(π/6)=1/2

4. Multiply the values together.

(−√(,2)/2)*(√(,3)/2)=−√(,6)/4

(√(,2)/2)*(1/2)=√(,2)/4

5. Combine the terms over the common denominator.

−√(,6)/4+√(,2)/4=(√(,2)−√(,6))/4

Final Answer

cos((3*π)/4−π/6)=(√(,2)−√(,6))/4

Want more problems? Check here!