Answer 1 To find the tangent of $45^\circ$ on the unit circle, we use the fact that $\tan \theta = \frac{\sin \theta}{\cos \theta}$. At $45^\circ$, $\sin 45^\circ = \frac{\sqrt{2}}{2}$ and $\cos 45^\circ = \frac{\sqrt{2}}{2}$. Therefore, $ \tan...

Answer 1 Given that $\sec \theta = 3$, we know that: $\sec \theta = \frac{1}{\cos \theta}$Solving for $\cos \theta$, we get:$\cos \theta = \frac{1}{3}$Using $\cos^{-1}(\frac{1}{3})$, we find:$\theta = \cos^{-1}(\frac{1}{3})$Converting to...

Answer 1 Given an angle \( \theta = \frac{\pi}{4} \), find the sine and cosine of the angle on the unit circle. Using the unit circle, the coordinates of the point at \( \theta = \frac{\pi}{4} \) are given by: \( (\cos(\frac{\pi}{4}),...

Answer 1 We start by locating the angle $\theta = 135°$ on the unit circle.Since $135°$ is in the second quadrant, we use the reference angle $45°$ to find the values. The coordinates of the point on the unit circle at this angle are $\left(...