Explore the unit circle and its relationship to angles, radians, trigonometric ratios, and coordinates in the coordinate plane.
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Answer 1 $ \text{One effective method is to use mnemonic devices and repetition.} $ $ \text{For instance, you can remember the coordinates for special angles, like } \theta = 0, \frac{\pi}{6}, \frac{\pi}{4}, \frac{\pi}{3}, \frac{\pi}{2} \text{ and so...
Answer 1 To find the sine, cosine, and tangent of the angle $\frac{5\pi}{4}$ radians, we need to locate the point on the unit circle corresponding to this angle.First, let's convert $\frac{5\pi}{4}$ radians to degrees. We know that $\pi$ radians is...
Answer 1 To determine the location of $-\pi/2$ on a unit circle, we follow these steps:1. Understand that the unit circle is a circle with a radius of 1 centered at the origin (0,0) in the coordinate plane.2. The angle $-\pi/2$ is measured in radians...
Answer 1 For the angle $\theta = \frac{5\pi}{6}$: The reference angle is $\pi - \frac{5\pi}{6} = \frac{\pi}{6}$. In the second quadrant, sine is positive, cosine is negative, and tangent is negative. Thus, the values are: $\sin(\frac{5\pi}{6}) =...
Answer 1 $Ways to Memorize the Unit Circle$Explanation with Examples:The unit circle is a circle with a radius of 1 centered at the origin (0,0) in the coordinate plane. To memorize the unit circle, follow these steps.1. Know the Key Angles:Memorize...
Answer 1 Given an angle of \( \theta = 45^{\circ} \). To find the coordinates of the point on the unit circle:The coordinates of any point on the unit circle can be found using the formulas:\[ x = \cos(\theta) \]\[ y = \sin(\theta) \]Using \( \theta...