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Answer 1 Given an angle \( \theta \) in the complex plane, the unit circle can be used to find the cosine of the angle. The cosine of the angle \( \theta \) is the x-coordinate of the point where the terminal side of the angle intersects the unit...
Answer 1 We are given the point $(\sqrt{3}/2, 1/2)$ on the unit circle. To find the corresponding angle, we use the following trigonometric relationships: $x = \cos(\theta)$$y = \sin(\theta)$Thus, we have:$\cos(\theta) = \sqrt{3}/2$$\sin(\theta) =...
Answer 1 Let's consider a point $P(\cos\theta, \sin\theta)$ on the unit circle where $\theta = \frac{5\pi}{6}$. To find the coordinates and verify trigonometric identities:First, we calculate the coordinates:$P = (\cos \frac{5\pi}{6}, \sin...
Answer 1 To find the cosine of the angle \( \frac{\pi}{3} \) on the unit circle, we need to locate this angle on the circle. The angle \( \frac{\pi}{3} \) corresponds to 60 degrees. On the unit circle, the coordinates of the point at angle \(...
Answer 1 To find the angles $\theta$ such that $\cos(\theta) = -\frac{1}{2}$, we start by identifying the quadrants where $\cos(\theta)$ is negative. Cosine is negative in the second and third quadrants. First, we find the reference angle:...
Answer 1 To find the coordinates of a point on the unit circle, we use the trigonometric functions sine and cosine.The angle given is $45^{\circ}$.Using the unit circle properties:$x = \cos 45^{\circ} = \frac{\sqrt{2}}{2}$$y = \sin 45^{\circ} =...