To help Mrs. Owen find \( \cos 300^\circ \) using the Unit Circle, let's follow these steps:
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Understanding the Unit Circle: The Unit Circle is a circle with a radius of 1 centered at the origin (0, 0) of a coordinate plane. The angle is measured from the positive x-axis, rotating counterclockwise for positive angles and clockwise for negative angles.
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Identifying the Angle: The angle \( 300^\circ \) is greater than \( 270^\circ \) and less than \( 360^\circ \). This means it is located in the fourth quadrant of the Unit Circle.
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Finding the Reference Angle: The reference angle is the acute angle formed with the x-axis. To find the reference angle for \( 300^\circ \), we can subtract it from \( 360^\circ \): \[ 360^\circ - 300^\circ = 60^\circ. \] Thus, the reference angle is \( 60^\circ \).
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Finding the Cosine Value: In the Unit Circle, the coordinates of the angle \( 300^\circ \) correspond to \( (x, y) \), where \( x = \cos 300^\circ \) and \( y = \sin 300^\circ \). Since \( 300^\circ \) is in the fourth quadrant, the cosine value is positive.
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Using the Reference Angle: The cosine of \( 300^\circ \) is the same as the cosine of its reference angle \( 60^\circ \): \[ \cos 60^\circ = \frac{1}{2}. \] Since \( 300^\circ \) is in the fourth quadrant, we have: \[ \cos 300^\circ = \cos 60^\circ = \frac{1}{2}. \]
So, the answer is: \[ \cos 300^\circ = \frac{1}{2}. \]
By remembering these steps, Mrs. Owen can effectively use the Unit Circle to find cosine values for various angles!