Simplify sec((7pi)/4)

Problem

sec((7*π)/4)

Solution

1. Identify the reference angle for the given angle (7*π)/4 Since the angle is in the fourth quadrant, the reference angle is 2*π−(7*π)/4=π/4

2. Determine the sign of the secant function in the fourth quadrant. In the fourth quadrant, the cosine function is positive, which means its reciprocal, the secant function, is also positive.

3. Apply the definition of secant as the reciprocal of cosine.

sec((7*π)/4)=1/cos((7*π)/4)

4. Evaluate the cosine of the angle using the reference angle.

cos((7*π)/4)=cos(π/4)=√(,2)/2

5. Calculate the reciprocal to find the final value.

sec((7*π)/4)=1/√(,2)/2=2/√(,2)=√(,2)

Final Answer

sec((7*π)/4)=√(,2)

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