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Ch. 1 - Trigonometric Functions
Lial - Trigonometry 12th Edition
Lial12th EditionTrigonometryISBN: 9780136552161, 9780135440780, 9780136881117, 9780135440827, 9780135924891Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoLial 12th EditionCh. 1 - Trigonometric FunctionsProblema 64
Capitolo 2, Problema 64

Find the indicated function value. If it is undefined, say so. See Example 4. sin 90°

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Recall that the sine function, \(\sin \theta\), gives the ratio of the length of the side opposite the angle \(\theta\) to the hypotenuse in a right triangle, or equivalently, the y-coordinate of the point on the unit circle at angle \(\theta\).
Identify the angle given: here, the angle is \(90^\circ\), which corresponds to the point on the unit circle at the top of the circle.
On the unit circle, the coordinates at \(90^\circ\) are \((0, 1)\), where the x-coordinate is \(\cos 90^\circ\) and the y-coordinate is \(\sin 90^\circ\).
Therefore, \(\sin 90^\circ\) is equal to the y-coordinate of this point, which is 1.
Conclude that \(\sin 90^\circ\) is defined and its value is 1.

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Definition of the Sine Function

The sine function relates an angle in a right triangle to the ratio of the length of the side opposite the angle to the hypotenuse. It is also defined on the unit circle as the y-coordinate of the point corresponding to the angle measured from the positive x-axis.
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Graph of Sine and Cosine Function

Special Angles and Their Sine Values

Certain angles, like 0°, 30°, 45°, 60°, and 90°, have well-known sine values that are often memorized. For example, sin 90° equals 1 because at 90°, the point on the unit circle is at (0,1), making the sine value the maximum possible.
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Sine, Cosine, & Tangent of 30°, 45°, & 60°

Domain and Range of the Sine Function

The sine function is defined for all real numbers (angles), so sin 90° is defined. Its range is between -1 and 1, inclusive, meaning sine values cannot be greater than 1 or less than -1.
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Domain and Range of Function Transformations
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