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cos -30° tan 90⁰

cos -30° tan 90⁰

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section6.6: Additional Trigonometric Graphs
Problem 60E
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The image contains two mathematical expressions pertaining to trigonometric functions. 1. **cos -30°** 2. **tan 90°** These expressions are commonly found in trigonometry problems. Here's an explanation of each: 1. **cos -30°:** - In trigonometry, the cosine function cosine (cos) of an angle in a right-angled triangle is the ratio of the adjacent side to the hypotenuse. - When the angle is negative, it implies that the measurement is taken in the clockwise direction. - Cosine of negative angles can be deduced using the property: cos(-θ) = cos(θ). Therefore, cos(-30°) = cos(30°). - The value of cos(30°) is √3/2. 2. **tan 90°:** - The tangent function (tan) of an angle in a right-angled triangle is the ratio of the opposite side to the adjacent side. - tan(90°) is a special case. In the unit circle, at 90°, the ratio of the opposite to the adjacent side approaches infinity because the adjacent side (cosine component) is zero and the opposite side (sine component) is 1. - Thus, tan(90°) is undefined because division by zero is undefined. These explanations can be used to elucidate the properties and values of trigonometric functions for specific angles.
Transcribed Image Text:The image contains two mathematical expressions pertaining to trigonometric functions. 1. **cos -30°** 2. **tan 90°** These expressions are commonly found in trigonometry problems. Here's an explanation of each: 1. **cos -30°:** - In trigonometry, the cosine function cosine (cos) of an angle in a right-angled triangle is the ratio of the adjacent side to the hypotenuse. - When the angle is negative, it implies that the measurement is taken in the clockwise direction. - Cosine of negative angles can be deduced using the property: cos(-θ) = cos(θ). Therefore, cos(-30°) = cos(30°). - The value of cos(30°) is √3/2. 2. **tan 90°:** - The tangent function (tan) of an angle in a right-angled triangle is the ratio of the opposite side to the adjacent side. - tan(90°) is a special case. In the unit circle, at 90°, the ratio of the opposite to the adjacent side approaches infinity because the adjacent side (cosine component) is zero and the opposite side (sine component) is 1. - Thus, tan(90°) is undefined because division by zero is undefined. These explanations can be used to elucidate the properties and values of trigonometric functions for specific angles.
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