Explore the unit circle and its relationship to angles, radians, trigonometric ratios, and coordinates in the coordinate plane.
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Answer 1 Given an angle $\theta$ in the flipped unit circle, where the x-values represent the sine of the angle and the y-values represent the cosine of the angle, find the sine and cosine of $\theta = \frac{5\pi}{4}$.First, note that $\theta =...
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Answer 1 First, we need to locate the angle 45° on the unit circle. The coordinates of this angle on the unit circle are (√2/2, √2/2). The sine of the angle is the y-coordinate of the point on the unit circle corresponding to that angle.Therefore,...
Answer 1 To find the exact values of $\cot$ for specific angles on the unit circle, let's consider the angle $\theta = \frac{11\pi}{6}$. Step 1: Identify the coordinates on the unit circle: The angle $\theta = \frac{11\pi}{6}$ corresponds to the...
Answer 1 To find the value of $\cos(-\pi/3)$ on the unit circle, we should first recall the basic properties of the cosine function and the unit circle:1. The cosine function is an even function, meaning $\cos(-x) = \cos(x)$.2. Therefore,...
Answer 1 The general equation of a circle with center at $(h, k)$ and radius $r$ is: $(x - h)^2 + (y - k)^2 = r^2$ Here, $h = 3$, $k = 4$, and $r = 5$. Substitute these values into the equation: $(x - 3)^2 + (y - 4)^2 = 5^2$ Simplifying further: $(x...