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Ch. 1 - Angles and the Trigonometric Functions
Blitzer - Trigonometry 3rd Edition
Blitzer3rd EditionTrigonometryISBN: 9780137316601Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoBlitzer 3rd EditionCh. 1 - Angles and the Trigonometric FunctionsProblema 85
Capitolo 1, Problema 85

Use the circle shown in the rectangular coordinate system to solve Exercises 81–86. Find two angles, in radians, between -2𝜋 and 2𝜋 such that each angle's terminal side passes through the origin and the given point.

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Identify the coordinates of the given point on the circle. Here, the point K is located at the top of the circle on the positive y-axis, so its coordinates are (0, 1).
Recall that the angle in standard position is measured from the positive x-axis counterclockwise. Since the point is on the positive y-axis, the reference angle is \( \frac{\pi}{2} \).
Find the two angles between \(-2\pi\) and \(2\pi\) whose terminal sides pass through the point (0, 1). One angle is the positive angle \( \frac{\pi}{2} \).
The other angle is the negative angle that corresponds to the same terminal side, which is found by subtracting \( 2\pi \) from \( \frac{\pi}{2} \), giving \( \frac{\pi}{2} - 2\pi = -\frac{3\pi}{2} \).
Thus, the two angles in radians between \(-2\pi\) and \(2\pi\) are \( \frac{\pi}{2} \) and \( -\frac{3\pi}{2} \).

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Unit Circle and Coordinates

The unit circle is a circle with radius 1 centered at the origin of the coordinate system. Points on the unit circle correspond to angles measured from the positive x-axis, and their coordinates (x, y) represent the cosine and sine of those angles, respectively.
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Introduction to the Unit Circle

Angles in Standard Position and Radians

An angle in standard position has its vertex at the origin and its initial side along the positive x-axis. Angles are measured in radians, where 2π radians correspond to a full circle. Negative angles represent clockwise rotation, and positive angles represent counterclockwise rotation.
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Drawing Angles in Standard Position

Finding Coterminal Angles

Coterminal angles share the same terminal side but differ by full rotations of 2π radians. To find two angles between -2π and 2π with the same terminal side, add or subtract multiples of 2π from a given angle, ensuring the angles fall within the specified range.
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Coterminal Angles
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