Find the Exact Value sec(3pi)

Problem

sec(3*π)

Solution

1. Identify the period of the secant function. The secant function, sec(θ) has a period of 2*π

2. Simplify the angle by subtracting the period. Since 3*π is greater than 2*π we can subtract 2*π to find a coterminal angle.

θ=3*π−2*π=π

3. Apply the definition of secant in terms of cosine.

sec(π)=1/cos(π)

4. Evaluate the cosine of the simplified angle. On the unit circle, the coordinates at π radians are (−1,0) so cos(π)=−1

sec(π)=1/(−1)

5. Calculate the final result.

sec(π)=−1

Final Answer

sec(3*π)=−1

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