Answer: To find the value of sec(270°), we need to understand the relationship between the secant function and the cosine function. The secant function (sec) is the reciprocal of the cosine function (cos).
On the unit circle, the cosine of an angle is the x-coordinate of the point on the unit circle corresponding to that angle. For example:
- At 0°, the cosine is 1, as the corresponding point on the unit circle is (1, 0).
- At 90°, the cosine is 0, as the corresponding point on the unit circle is (0, 1).
- At 180°, the cosine is -1, as the corresponding point on the unit circle is (-1, 0).
- At 270°, the cosine is 0, as the corresponding point on the unit circle is (0, -1).
Now, let's find the secant of 270°, which is the reciprocal of the cosine at that angle:
sec(270°) = 1 / cos(270°)
Since cos(270°) is 0, the secant of 270° will be undefined because we cannot divide by zero.
In summary, the value of sec(270°) is undefined because the cosine of 270° is 0, and the secant function is the reciprocal of the cosine function. The point (0, -1) on the unit circle shows that the cosine at 270° is 0, which leads to an undefined value for sec(270°).