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Answer 1 Given that \( \theta \) is an angle in the unit circle such that its terminal side passes through the point \((a,b)\): The coordinates \((a, b)\) on the unit circle imply that \(a = \cos(\theta)\) and \(b = \sin(\theta)\). Since the line...
Answer 1 To find the sine and cosine of a 45-degree angle, we can use the unit circle. A 45-degree angle corresponds to $\frac{\pi}{4}$ radians.On the unit circle, the coordinates for $\frac{\pi}{4}$ are given by $\left( \cos \frac{\pi}{4}, \sin...
Answer 1 To find the coordinates of the point on the unit circle at an angle of $\frac{\pi}{3}$ radians, we use the trigonometric functions cosine and sine.For an angle $\theta = \frac{\pi}{3}$:$ \cos \left( \frac{\pi}{3} \right) = \frac{1}{2} $$...
Answer 1 To find the value of $ tan(\frac{\pi}{4}) $ using the unit circle, we need to consider the coordinates of the point on the unit circle at the angle $ \frac{\pi}{4} $. The coordinates of this point are $ (\frac{\sqrt{2}}{2},...
Answer 1 Given an angle \( \theta = \frac{5\pi}{4} \), find the values of \( \sin(\theta) \), \( \cos(\theta) \), and \( \tan(\theta) \). First, determine the reference angle in the unit circle. \( \theta = \frac{5\pi}{4} \) is in the third quadrant....
Answer 1 To locate the position of $-\pi/2$ on the unit circle, we need to understand the unit circle itself. The circle has a radius of 1 and is centered at the origin (0,0).1. Start from the positive x-axis and move counterclockwise.2. A negative...