Find the Exact Value sin((7pi)/6)cos(pi/6)

Problem

sin((7*π)/6)*cos(π/6)

Solution

1. Identify the reference angle for (7*π)/6 Since (7*π)/6=π+π/6 the angle is in the third quadrant where the sine function is negative.

2. Evaluate the sine term using the reference angle π/6

sin((7*π)/6)=−sin(π/6)

sin((7*π)/6)=−1/2

3. Evaluate the cosine term for the angle π/6 which is in the first quadrant.

cos(π/6)=√(,3)/2

4. Multiply the two values together to find the final product.

(−1/2)⋅(√(,3)/2)=−√(,3)/4

Final Answer

sin((7*π)/6)*cos(π/6)=−√(,3)/4

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