Find the Exact Value sin(-11/6*pi)

Problem

sin(−(11*π)/6)

Solution

1. Identify the angle and find its coterminal equivalent within the standard interval [0,2*π] by adding 2*π

θ=−(11*π)/6+2*π

θ=−(11*π)/6+(12*π)/6

θ=π/6

2. Determine the quadrant of the coterminal angle π/6 which is in Quadrant I where all trigonometric functions are positive.

sin(−(11*π)/6)=sin(π/6)

3. Evaluate the sine of the reference angle π/6 using the unit circle or special right triangles.

sin(π/6)=1/2

Final Answer

sin(−(11*π)/6)=1/2

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