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Given that \( \theta \) is an angle in the unit circle such that its terminal side passes through the point (a,b) If the line passing through (a,b) and the origin makes an angle \( \alpha \) with the x-axis, find the values of \( \sin(\alpha) \), \( \cos

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...

Find the sine and cosine of a 45-degree angle

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...

Find the value of tan(π/4) using the unit circle

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},...

Find the trigonometric values for an angle in the unit circle

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....

Determining the Position of -π/2 on the Unit Circle

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...