Simplify sec(150)

Problem

sec(150)

Solution

1. Identify the reference angle for 150 Since 150 is in the second quadrant, the reference angle is 180−150=30

2. Determine the sign of the secant function in the second quadrant. In the second quadrant, cosine is negative, and since sec(θ)=1/cos(θ) secant is also negative.

3. Apply the reference angle and sign to the expression.

sec(150)=−sec(30)

4. Evaluate the secant of the reference angle. Since cos(30)=√(,3)/2 the secant is the reciprocal.

sec(30)=2/√(,3)

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

2/√(,3)⋅√(,3)/√(,3)=(2√(,3))/3

6. Combine the value with the negative sign determined in step 2.

sec(150)=−(2√(,3))/3

Final Answer

sec(150)=−(2√(,3))/3

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