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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...
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\...