Ai Tools

Answer 1 $\text{Consider the point where the angle is } 60^\circ \text{ on the unit circle.}$ $\text{The cosine of } 60^\circ \text{ is given by } \cos(60^\circ) = \frac{1}{2}. $$\text{Therefore, the cosine value at } 60^\circ \text{ on the unit...

Answer 1 First, locate the angle $\frac{5\pi}{6}$ on the unit circle.The angle $\frac{5\pi}{6}$ is in the second quadrant.In the second quadrant, sine is positive and cosine is negative.The reference angle for $\frac{5\pi}{6}$ is $\pi -...

Answer 1 Consider the angle $\theta = \frac{3\pi}{4}$ on the unit circle.First, determine the reference angle. The reference angle for $\frac{3\pi}{4}$ is $\frac{\pi}{4}$.Since $\frac{3\pi}{4}$ is in the second quadrant, tangent is negative.We know...

Answer 1 Consider the point $P(\frac{1}{2}, \frac{\sqrt{3}}{2})$ on the unit circle. Determine the cosine of the angle $\theta$ corresponding to this point.Solution:On the unit circle, the coordinates of a point $P(x, y)$ correspond to $(\cos \theta,...

Answer 1 To find the slope of the tangent line to the unit circle at the point where $\theta = \frac{\pi}{4}$, we start by finding the coordinates of the point on the unit circle.At $\theta = \frac{\pi}{4}$, the coordinates are: $...