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Ch. 2 - Acute Angles and Right Triangles
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. 2 - Acute Angles and Right TrianglesProblema 51
Capitolo 3, Problema 51

Give the exact value of each expression. See Example 5. sin 30°

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1
Recall the definition of the sine function in a right triangle: \(\sin \theta = \frac{\text{opposite side}}{\text{hypotenuse}}\).
Recognize that 30° is a special angle in trigonometry, often associated with well-known exact values.
Use the known exact value for \(\sin 30^\circ\), which comes from the properties of a 30°-60°-90° triangle.
Recall that in a 30°-60°-90° triangle, the side opposite 30° is half the length of the hypotenuse.
Therefore, \(\sin 30^\circ = \frac{1}{2}\).

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Definition of the Sine Function

The sine of an angle in a right triangle is the ratio of the length of the side opposite the angle to the hypotenuse. It is a fundamental trigonometric function used to relate angles to side lengths.
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Graph of Sine and Cosine Function

Special Angles and Their Exact Values

Certain angles like 30°, 45°, and 60° have well-known exact sine values derived from special triangles. For example, sin 30° equals 1/2, which is often memorized or derived from an equilateral triangle split in half.
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45-45-90 Triangles

Using Reference Triangles to Find Exact Values

Reference triangles, such as the 30°-60°-90° triangle, help determine exact trigonometric values without a calculator. Understanding their side ratios allows for precise computation of sine, cosine, and tangent values.
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Reference Angles on the Unit Circle
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