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Answer 1 $Method\ 1: \ Use\ Symmetry$ $Explanation: \ The\ unit\ circle\ is\ symmetric\ about\ the\ x-axis,\ y-axis,\ and\ the\ origin.\ By\ knowing\ the\ key\ points\ in\ the\ first\ quadrant,\ you\ can\ easily\ deduce\ the\ corresponding\ points\...
Answer 1 To find the cosine and sine of $ \frac{\pi}{10} $ on the unit circle, we use the following steps. Since $ \frac{\pi}{10} $ is an angle in radians, we can find its coordinates on the unit circle. The coordinates of an angle $ \theta $ on the...
Answer 1 To find the sine, cosine, and tangent values for $45^\circ$ on the unit circle, we use the following formulas:$\sin 45^\circ = \frac{1}{\sqrt{2}}$$\cos 45^\circ = \frac{1}{\sqrt{2}}$$\tan 45^\circ = 1$Therefore, the sine, cosine, and tangent...
Answer 1 First, understand the basics of the unit circle. The unit circle is a circle with a radius of 1, centered at the origin (0, 0) of a coordinate plane.$x^2 + y^2 = 1$Next, memorize key angles and their coordinates in both degrees and radians....
Answer 1 To find the value of $\tan \theta $, we use the fact that tan is defined as the ratio of the y-coordinate to the x-coordinate on the unit circle. Given the point $\left( -\frac{1}{2}, -\frac{\sqrt{3}}{2} \right)$, we have: $\tan \theta =...
Answer 1 Using the unit circle, we know that the angle $\frac{\pi}{3}$ corresponds to 60 degrees. From the unit circle properties: The coordinates at $\frac{\pi}{3}$ are $(\frac{1}{2}, \frac{\sqrt{3}}{2})$.So, the cosine of $\frac{\pi}{3}$ is...