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Answer 1 To find the trigonometric values of an angle of 150 degrees on the unit circle, we can use the angle relationship and symmetry of the unit circle. 1. Convert the angle to radians: $150° = \frac{5\pi}{6}$ radians. 2. Recall that on the unit...
Answer 1 To find the secant of the angle $\theta = 45^{\circ}$ on the unit circle, we use the relationship between secant and cosine.The secant of an angle is the reciprocal of its cosine:$\sec(\theta) = \frac{1}{\cos(\theta)}$.For $\theta =...
Answer 1 Given a point $P(a, b)$ on the unit circle, find the value of $\tan(\theta)$ where $\theta$ is the angle formed by the radius to the point P and the positive x-axis. Solution: We know that $\tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)}$....
Answer 1 To solve this, we need to find the sine, cosine, and tangent values for the angle $\frac{\pi}{6}$ on the unit circle.The angle $\frac{\pi}{6}$ corresponds to 30 degrees.Using the unit circle, we know that: $ \sin \left( \frac{\pi}{6} \right)...
Answer 1 Given the coordinates $\left( \frac{1}{2}, \frac{\sqrt{3}}{2} \right)$ on the unit circle, we know that the x-coordinate represents $\cos(\theta)$. Therefore: $ \cos(\theta) = \frac{1}{2} $ The secant function is the reciprocal of the cosine...
Answer 1 Given the point on the unit circle corresponding to $\\theta$ is $ (\\frac{1}{2}, \\frac{\\sqrt{3}}{2})$, we know $\\cos(\\theta) = \\frac{1}{2}.$ Therefore, $\\sec(\\theta) = \\frac{1}{\\cos(\\theta)} = \\frac{1}{\\frac{1}{2}} = 2.$ Answer...