Find the Exact Value sin((7pi)/3)

Problem

sin((7*π)/3)

Solution

1. Find the coterminal angle by subtracting 2*π from the given angle to find an equivalent angle within the standard interval [0,2*π]

(7*π)/3−2*π=(7*π)/3−(6*π)/3

(7*π)/3−(6*π)/3=π/3

2. Identify the reference angle and the quadrant. The angle π/3 is in the first quadrant, where all trigonometric functions are positive.

sin((7*π)/3)=sin(π/3)

3. Determine the exact value using the unit circle or special right triangles for the sine of 60^∘ or π/3 radians.

sin(π/3)=√(,3)/2

Final Answer

sin((7*π)/3)=√(,3)/2

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