91Ó°ÊÓ

To sketch the unit circle and the radius that makes an angle of \(\cos ^{-1} 0.1\) with the positive horizontal axis, follow these steps: 1. Draw a circle centered at the origin (0,0) with a radius of 1. 2. The cosine of the angle is 0.1, which is the x-coordinate of the point on the unit circle. 3. The x-coordinate of the point is 0.1. 4. By the equation \(x^2 + y^2 = 1\), the positive y-coordinate will be slightly below 1 when x=0.1. 5. Mark the point on the unit circle where the x-coordinate is 0.1 and the positive y-coordinate is slightly below 1. 6. Draw a line segment connecting the origin (0,0) to the marked point on the unit circle. Now, the unit circle and the radius with an angle of \(\cos^{-1}0.1\) are accurately sketched.