Find the Exact Value sin(5/12)

Problem

sin((5*π)/12)

Solution

1. Identify the angle in terms of known values. The angle (5*π)/12 can be expressed as the sum of two standard angles: (2*π)/12+(3*π)/12

2. Simplify the fractions to standard radian measures.

(2*π)/12=π/6

(3*π)/12=π/4

3. Apply the sum formula for sine, which is sin(A+B)=sin(A)*cos(B)+cos(A)*sin(B)

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

4. Substitute the exact values for the trigonometric functions of standard angles.

sin(π/6)=1/2

cos(π/4)=√(,2)/2

cos(π/6)=√(,3)/2

sin(π/4)=√(,2)/2

5. Multiply the terms.

1/2⋅√(,2)/2=√(,2)/4

√(,3)/2⋅√(,2)/2=√(,6)/4

6. Combine the fractions over a common denominator.

√(,2)/4+√(,6)/4=(√(,2)+√(,6))/4

Final Answer

sin((5*π)/12)=(√(,2)+√(,6))/4

Want more problems? Check here!