Find the Value Using the Unit Circle sin(-pi/3)

Problem

sin(−π/3)

Solution

1. Identify the angle −π/3 on the unit circle by moving clockwise from the positive xaxis.

2. Find the coterminal angle in the standard interval [0,2*π) by adding 2*π

−π/3+(6*π)/3=(5*π)/3

3. Determine the coordinates (x,y) at (5*π)/3 on the unit circle, which are (1/2,−√(,3)/2)

4. Apply the definition of the sine function on the unit circle, where sin(θ)=y

sin(−π/3)=−√(,3)/2

Final Answer

sin(−π/3)=−√(,3)/2

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