Evaluate the inverse trigonometric function. Give your answer to the nearest degree. (Enter only the number.)
cos^-1 (-1)
surely you know that cos(180°) = -1
so, arccos(-1) = 180°
To evaluate the inverse trigonometric function cos^-1(-1), we can start by recalling the definition of the inverse cosine function. The inverse cosine function, cos^-1(x) or arccos(x), gives us the angle whose cosine is equal to x.
In this case, we want to find the angle whose cosine is equal to -1. Since the cosine function represents the x-coordinate of a point on the unit circle, we can determine the angle by looking at the unit circle.
The unit circle is a circle with a radius of 1 centered at the origin (0,0) on a coordinate plane. The x-coordinate of a point on the unit circle represents the cosine value for the corresponding angle.
For cos^-1(-1), we are essentially looking for an angle whose cosine is -1. From the unit circle, we can see that the cosine is -1 at the angle 180 degrees (or π radians), which is at the point (-1,0) on the unit circle.
Therefore, the inverse cosine of -1 is 180 degrees or π radians.
Answer: 180