Explanation Given: The given figure is Definition used: The six trigonometric ratios: sin α = opposite hypotenuse cosec α = hypotenuse opposite cos α = adjacent hypotenuse sec α = hypotenuse adjacent tan α = opposite adjacent cot α = adjacent opposite Calculation: Let the unknown side in the triangle be a . In a right triangle, ( hypotenuse ) 2 = ( opposite ) 2 + ( adjacent ) 2 ( a ) 2 = x 2 + 2 2 a 2 = x 2 + 4 a = x 2 + 4 Thus we have From the figure, opposite = x , adjacent = 2 , hypotenuse = x 2 + 4

Elementary Geometry For College Students, 7e

7th Edition

ISBN: 9781337614085

Author: Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher: Cengage,

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Ratios

A ratio is a comparison between two numbers of the same kind. It represents how many times one number contains another. It also represents how small or large one number is compared to the other.

Trigonometric Ratios

Trigonometric ratios give values of trigonometric functions. It always deals with triangles that have one angle measuring 90 degrees. These triangles are right-angled. We take the ratio of sides of these triangles.

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Polygon with three sides, three angles, and three vertices. Based on the properties of each side, the types of triangles are scalene (triangle with three three different lengths and three different angles), isosceles (angle with two equal sides and two equal angles), and equilateral (three equal sides and three angles of 60°). The types of angles are acute (less than 90°); obtuse (greater than 90°); and right (90°).

Chapter 11.3, Problem 10E

To determine

To find:

The value for each of the six trigonometric ratios of angle α.

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Chapter 11.3, Problem 9E

Chapter 11.3, Problem 11E

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Chapter 11 Solutions

Elementary Geometry For College Students, 7e

Ch. 11.1 - In Exercises 1 to 6, find sin and sin for the...Ch. 11.1 - In Exercises 1 to 6, find sin and sin for the...Ch. 11.1 - In Exercises 1 to 6, find sin and sin for the...Ch. 11.1 - In Exercises 1 to 6, find sin and sin for the...Ch. 11.1 - In Exercises 1 to 6, find sin and sin for the...Ch. 11.1 - In Exercises 1 to 6, find sin and sin for the...Ch. 11.1 - In Exercises 7 to 14, use either Table 11.2 or a...Ch. 11.1 - In Exercises 7 to 14, use either Table 11.2 or a...Ch. 11.1 - Prob. 9E Ch. 11.1 - Prob. 10E

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