Concept explainers
To calculate: The tangent trigonometric function
Answer to Problem 39E
The tangent trigonometric function
Explanation of Solution
Given information:
The trigonometric functions
Formula used:
Coordinate plane is divided into four quadrants.
In the first quadrant all trigonometric functions that is
In the second quadrant only sine and cosecant trigonometric functions that is
In the third quadrant only tangent and cotangent trigonometric functions that is
In the fourth quadrant only cosine and secant trigonometric functions that is
The Pythagorean identity
Calculation:
Consider the provided trigonometric functions
To write the tangent function in terms of cosine trigonometric function.
Recall that
Rewrite
Recall the Pythagorean identity
Subtract
Since
Recall that coordinate plane is divided into four quadrants.
In the third quadrant only tangent and cotangent trigonometric functions that is
That is sine trigonometric function is negative.
Therefore,
Now, substitute the value of
Thus, the tangent trigonometric function
Chapter 6 Solutions
Precalculus: Mathematics for Calculus - 6th Edition
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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