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Answer 1 To find the equations of all circles on the unit circle, we start with the general form of a circle's equation:$ (x - h)^2 + (y - k)^2 = r^2$Since we are dealing with the unit circle, the radius r is 1. Thus, the equation simplifies to:$ (x...
Answer 1 To find the value of $\tan(\theta)$ where $\theta$ is a special angle on the unit circle, we use the definition $\tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)}$. For $\theta = \frac{\pi}{4}$, the sine and cosine values are both...
Answer 1 $\text{To memorize the unit circle, observe that it is divided into four quadrants. Each quadrant contains key angles: 0, } \frac{\pi}{6}, \frac{\pi}{4}, \frac{\pi}{3}, \frac{\pi}{2}, \pi, \frac{3\pi}{2}, \text{ and } 2\pi.$ $\text{For...
Answer 1 Using the unit circle, we can find the values of $\sin(\frac{\pi}{4})$ and $\cos(\frac{\pi}{4})$ by locating the angle $\frac{\pi}{4}$ radians. This angle corresponds to a 45-degree angle in the unit circle.At this angle, both the...
Answer 1 To find the cosine of $45^\circ$, we use the unit circle. On the unit circle, the coordinates of the point where the terminal side of the $45^\circ$ angle intersects the circle are $(\frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2})$. The cosine of an...
Answer 1 Let's determine the sine, cosine, and tangent values for the angle θ = 225° on the unit circle.First, convert the angle to radians: $ θ = 225° = \frac{225π}{180} = \frac{5π}{4} radians $Using the properties of the unit circle, we know: $...