Concept explainers
(a)
Find all the Trigonometric Function exists.
(a)
Answer to Problem 88E
Explanation of Solution
Given: the angle
Concept Used:
In mathematics, the trigonometric functions (also called circular functions, angle functions or goniometric functions) are real functions which relate an angle of a right-angled triangle to ratios of two side lengths. The most widely used trigonometric functions are the sine, the cosine, and the tangent. Their reciprocals are respectively the cosecant, the secant, and the cotangent,
For unit circle: Hypotenuse = Radius of the circle = 1
From the unit circle, we know that:
For he angle
Calculation:
Thus, all six trigonometric functions are
(b)
Which Trigonometric functions are positive and negative ?
(b)
Answer to Problem 88E
tan
Explanation of Solution
Given: the angle
Concept Used:
The angle
in the third quadrant, according to the sign convention rule, tangent and cotangent functions are only positive. Sine , Cosine , cosecant and secant all functions are negative. Now we can write: |
Calculation:
Thus, tan
Chapter 4 Solutions
Precalculus with Limits: A Graphing Approach
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- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning