Concept explainers
To calculate: The secant trigonometric function
Answer to Problem 42E
The secant 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
The reciprocal identity
Calculation:
Consider the provided trigonometric functions
To write the secant function in terms of sine trigonometric function.
Recall the reciprocal identity
Rewrite the cosine function in terms of sine function.
Recall the Pythagorean identity
Subtract
Since
Recall that coordinate plane is divided into four quadrants.
In the first quadrant all trigonometric functions that is
That is cosine trigonometric function is positive.
Therefore,
Now, substitute the value of
Thus, the secant trigonometric function
Chapter 6 Solutions
Precalculus: Mathematics for Calculus - 6th Edition
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