Final answer:
The value of sec(π) is -1, as it's the reciprocal of cos(π), which is -1. Therefore, the secant of π would be the reciprocal of -1, which is -1. Hence, the correct answer is b) -1
Step-by-step explanation:
The student has asked to evaluate the trigonometric function sec(π). To find the value of sec(π), we need to understand that sec(θ) is the reciprocal of cos(θ), so sec(π) = 1/cos(π). In the unit circle, π radians corresponds to the point (-1,0), which means the cosine at π is -1.
To evaluate the trigonometric function sec(π), we must first understand what the secant function represents. The secant of an angle θ, denoted sec(θ), is defined as the reciprocal of the cosine of that angle. sec(θ) = 1 / cos(θ) Now, we need to evaluate cos(π).
The angle π radians corresponds to 180 degrees, which is a straight angle. On the unit circle, the cosine of an angle represents the x-coordinate of the point where the terminal side of the angle intersects the unit circle. The cosine of π radians (or 180 degrees) is -1, as the point at this angle on the unit circle has coordinates (-1, 0). With this in mind: cos(π) = -1 To find sec(π), we take the reciprocal of cos(π): sec(π) = 1 / cos(π) = 1 / -1 = -1 Therefore, the correct answer is b) -1.
Therefore, the secant of π would be the reciprocal of -1, which is -1. Hence, the correct answer is b) -1