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Answer 1 To find the exact values of $\sin(\frac{7\pi}{6})$, $\cos(\frac{7\pi}{6})$, and $\tan(\frac{7\pi}{6})$ using the unit circle, we follow these steps: 1. Identify the reference angle: The reference angle for $\frac{7\pi}{6}$ is...
Answer 1 For $ 30^\circ $ on the unit circle:$ \sin(30^\circ) = \frac{1}{2} $$ \cos(30^\circ) = \frac{\sqrt{3}}{2} $$ \tan(30^\circ) = \frac{1}{\sqrt{3}} \text{ or } \frac{\sqrt{3}}{3} $Answer 2 At $ 30^circ $ on the unit circle:$ sin(30^circ) =...
Answer 1 To find the value of $ \tan(135^\circ) $ using the unit circle, we need to recall that $ \tan\theta $ is the ratio of the y-coordinate to the x-coordinate of the point where the terminal side of the angle intersects the unit circle.The angle...
Answer 1 Given the angles $ \theta_1, \theta_2, \theta_3 $ of the vertices of the triangle, the coordinates of the vertices on the unit circle are:Vertex 1: $ ( \cos(\theta_1), \sin(\theta_1) ) $Vertex 2: $ ( \cos(\theta_2), \sin(\theta_2) ) $Vertex...
Answer 1 Given: $ \sin(\theta)\cos(\theta) = \frac{1}{4} $ Using the double-angle identity: $ \sin(2\theta) = 2\sin(\theta)\cos(\theta) $ We have: $ \sin(2\theta) = 2 \times \frac{1}{4} = \frac{1}{2} $Thus: $ 2\theta = \sin^{-1}(\frac{1}{2}) $...
Answer 1 To find the value of $\sin(2x)$ and $\cos(2x)$ on the unit circle, we can utilize the double-angle formulas: $ \sin(2x) = 2\sin(x)\cos(x) $ $ \cos(2x) = \cos^2(x) - \sin^2(x) $ Given a point on the unit circle (a, b) where $a = \cos(x)$ and...