How do you evaluate sec(150°)?

To evaluate sec(150°), we first need to understand what secant means. The secant function is the reciprocal of the cosine function. Therefore, sec(θ) = 1/cos(θ).

Step-by-Step Evaluation

1. **Find cos(150°)**: The angle 150° is in the second quadrant, where cosine values are negative. We can use the reference angle, which is 180° - 150° = 30°. The cosine of 30° is √3/2, so:

cos(150°) = -cos(30°) = -√3/2

2. **Calculate sec(150°)**: Now that we have cos(150°), we can find sec(150°):

sec(150°) = 1/cos(150°) = 1/(-√3/2)

3. **Simplify the expression**: To simplify, multiply by the reciprocal:

sec(150°) = -2/√3

Final Result

To express this in a more standard form, you can rationalize the denominator:

sec(150°) = -2√3/3

Thus, the value of sec(150°) is -2√3/3.