Find the Exact Value sec(210)

Problem

sec(210)

Solution

1. Identify the reference angle by determining the distance from the nearest x-axis. Since 210 is in the third quadrant, subtract 180 from the angle.

210−180=30

2. Determine the sign of the secant function in the third quadrant. In the third quadrant, only tangent and cotangent are positive, so secant is negative.

sec(210)=−sec(30)

3. Recall the reciprocal identity for secant.

sec(30)=1/cos(30)

4. Substitute the known value for cos(30)=√(,3)/2 into the expression.

sec(210)=−1/√(,3)/2

5. Simplify the fraction by multiplying by the reciprocal.

sec(210)=−2/√(,3)

6. Rationalize the denominator by multiplying the numerator and denominator by √(,3)

sec(210)=−(2√(,3))/3

Final Answer

sec(210)=−(2√(,3))/3

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