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Answer 1 To find the angle where $\tan(\theta) = -1$ in the unit circle, we need to look for the values of $\theta$ where the tangent function is negative and equals -1.We know that $\tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)}$. For...
Answer 1 To find the exact values of trigonometric functions for $ \theta = \frac{5\pi}{6} $, we first recognize that this angle corresponds to a reference angle of $ \frac{\pi}{6} $ in the second quadrant.The coordinates of the point on the unit...
Answer 1 Given that $\theta = \frac{5\pi}{6}$, find the value of $\cos(\theta)$ on the unit circle. Step 1: Identify the reference angle. The reference angle for $\theta = \frac{5\pi}{6}$ is $\pi - \frac{5\pi}{6} = \frac{\pi}{6}$. Step 2: Determine...
Answer 1 $\text{To remember the angles and coordinates on a unit circle, follow these steps:}$ $1.\ \text{Divide the circle into four quadrants, each covering 90 degrees or } \frac{\pi}{2}$ $2.\ \text{Identify the key angles in radians: } 0,...
Answer 1 To find the exact values of $\cos \frac{7\pi}{6}$ and $\sin \frac{7\pi}{6}$, we start by locating the angle on the unit circle. The angle $\frac{7\pi}{6}$ is in the third quadrant.We know that $\frac{7\pi}{6} = \pi + \frac{\pi}{6}$. This...
Answer 1 Consider the angle $45^\circ$ (or $\frac{\pi}{4}$ radians) on the unit circle. Find the sine, cosine, and tangent values for this angle.Step 1: Identify the coordinates on the unit circle for the angle $45^\circ$. The coordinates are...