Find the Exact Value sec(150)

Problem

sec(150)

Solution

1. Identify the reference angle for 150 by subtracting it from 180

(θ_ref)=180−150=30

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

sec(150)=−sec(30)

3. Recall the value of cos(30) to find its reciprocal.

cos(30)=√(,3)/2

4. Calculate the reciprocal to find sec(30)

sec(30)=2/√(,3)

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

2/√(,3)⋅√(,3)/√(,3)=(2√(,3))/3

6. Apply the negative sign determined in step 2.

sec(150)=−(2√(,3))/3

Final Answer

sec(150)=−(2√(,3))/3

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