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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...
Answer 1 To find the cosine values for angles on the unit circle, we first identify the angles and then use the unit circle definition. Example angles: \(\theta = \frac{\pi}{3}, \theta = \frac{5\pi}{6}, \theta = \frac{7\pi}{4}\). For \(\theta =...
Answer 1 To find the value of $\tan(\theta)$ for $\theta = \frac{7\pi}{4}$ using the unit circle, we first need to determine the coordinates of the point on the unit circle corresponding to $\theta = \frac{7\pi}{4}$. $\theta = \frac{7\pi}{4}$...