Draw a unit circle and mark each point on the circle that has an x-coordinate equal to - 1.
180^(∘)+360^(∘) * n, for any integer n
Practice makes perfect
We want to find all the angles whose cosine is - 1. Since we know the value of cosine but not the value of the angle, the process of finding the missing value uses an inverse trigonometric function.
cos^(- 1) (- 1)First, we need to draw the angle in standard position on a unit circle. The cosine of an angle in standard position is the x-coordinate of the point of intersection of its terminal side and the unit circle. We will consider the points on the unit circle that have an x-coordinate of - 1.
We see that the desired angle is 180^(∘). Finally, keep in mind that if we add or subtract a multiple of 360^(∘), the terminal side of the angle will be in the same position. Therefore, the cosine of the resulting angles will also be - 1.
180^(∘)+360^(∘) * n,
wheren is any integer
