Find the Value Using the Unit Circle sec((2pi)/3)

Problem

sec((2*π)/3)

Solution

1. Identify the angle (2*π)/3 on the unit circle, which is located in the second quadrant.

2. Determine the coordinates (x,y) for the angle (2*π)/3 which are (−1/2,√(,3)/2)

3. Recall the definition of the secant function in terms of the unit circle coordinates, where sec(θ)=1/x

4. Substitute the xcoordinate into the definition: sec((2*π)/3)=1/(−1/2)

5. Simplify the expression by multiplying by the reciprocal.

Final Answer

sec((2*π)/3)=−2

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