Find the Exact Value sin((35pi)/6)

Problem

sin((35*π)/6)

Solution

1. Find the coterminal angle by subtracting multiples of 2*π (which is (12*π)/6 from the given angle until it is within the interval [0,2*π)

(35*π)/6−2*π=(23*π)/6

(23*π)/6−2*π=(11*π)/6

2. Identify the quadrant for the angle (11*π)/6 Since (3*π)/2<(11*π)/6<2*π the angle is in Quadrant IV.

3. Determine the reference angle for an angle in Quadrant IV using the formula (θ_ref)=2*π−θ

(θ_ref)=2*π−(11*π)/6=π/6

4. Apply the sine function to the reference angle and determine the sign based on the quadrant. In Quadrant IV, the sine value is negative.

sin((11*π)/6)=−sin(π/6)

5. Evaluate the sine of the reference angle π/6

sin(π/6)=1/2

sin((35*π)/6)=−1/2

Final Answer

sin((35*π)/6)=−1/2

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