Find the Exact Value sec((3pi)/4)

Problem

sec((3*π)/4)

Solution

1. Identify the relationship between the secant function and the cosine function using the reciprocal identity.

sec(θ)=1/cos(θ)

2. Determine the reference angle for (3*π)/4 by subtracting it from π

Reference Angle=π−(3*π)/4=π/4

3. Evaluate the cosine of the reference angle using known values from the unit circle.

cos(π/4)=√(,2)/2

4. Determine the sign of the cosine function in the second quadrant, where (3*π)/4 is located.

cos((3*π)/4)=−√(,2)/2

5. Substitute the cosine value back into the reciprocal identity to find the secant.

sec((3*π)/4)=1/(−√(,2)/2)

6. Simplify the expression by multiplying by the reciprocal and rationalizing the denominator.

sec((3*π)/4)=−2/√(,2)=−√(,2)

Final Answer

sec((3*π)/4)=−√(,2)

Want more problems? Check here!