Evaluate sec(150 degrees )

Problem

sec(150)

Solution

1. Identify the relationship between the secant function and the cosine function.

sec(θ)=1/cos(θ)

2. Determine the reference angle for 150 Since 150 is in the second quadrant, the reference angle is 180−150

(θ_ref)=30

3. Evaluate the cosine of 150 In the second quadrant, cosine is negative.

cos(150)=−cos(30)

4. Substitute the known value for cos(30) which is √(,3)/2

cos(150)=−√(,3)/2

5. Calculate the secant by taking the reciprocal of the cosine value.

sec(150)=1/(−√(,3)/2)

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

sec(150)=−2/√(,3)⋅√(,3)/√(,3)

sec(150)=−(2√(,3))/3

Final Answer

sec(150)=−(2√(,3))/3

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