Concept explainers
To calculate: The value of trigonometric ratios
Answer to Problem 10E
The value of trigonometric ratiosare
Explanation of Solution
Given information:
The right angle triangle with length of its sides and angles
Formula used:
The trigonometric ratios for a right angle triangle are defined as,
Calculation:
The right angle triangle with length of its sides and angles
First consider the opposite, adjacent and hypotenuse with respect to angle
Observe that opposite side is of length 4 units and hypotenuse has length 7 units.
Now, let the length of adjacent side be x , as it is a right angle triangle so,
Therefore, length of adjacent side is
Recall that the sine trigonometric ratio for a right angle triangle is defined as,
Apply it, to estimate the value of trigonometric ratios,
The value of sine function is,
Second consider the opposite, adjacent and hypotenuse with respect to angle
Observe that adjacent side is of length 4 units and hypotenuse has length 7 units.
Now, let the length of opposite side be x , as it is a right angle triangle so,
Therefore, length of opposite side is
Recall that the cosine trigonometric ratio for a right angle triangle is defined as,
Apply it, to estimate the value of trigonometric ratios,
The value of cosine function is,
Thus, the value of trigonometric ratiosare
To calculate: The value of trigonometric ratios
Answer to Problem 10E
The value of trigonometric ratiosare
Explanation of Solution
Given information:
The right angle triangle with length of its sides and angles
Formula used:
The trigonometric ratios for a right angle triangle are defined as,
Calculation:
The right angle triangle with length of its sides and angles
First consider the opposite, adjacent and hypotenuse with respect to angle
Observe that opposite side is of length 4 units and hypotenuse has length 7 units.
Now, let the length of adjacent side be x , as it is a right angle triangle so,
Therefore, length of adjacent side is
Recall that the tangent trigonometric ratio for a right angle triangle is defined as,
Apply it, to estimate the value of trigonometric ratios,
The value of tangent function is,
Second consider the opposite, adjacent and hypotenuse with respect to angle
Observe that adjacent side is of length 4 units and hypotenuse has length 7 units.
Now, let the length of opposite side be x , as it is a right angle triangle so,
Therefore, length of opposite side is
Recall that the cosine trigonometric ratios for a right angle triangle is defined as,
Apply it, to estimate the value of trigonometric ratios,
The value of cotangent function is,
Thus, the value of trigonometric ratiosare
To calculate: The value of trigonometric ratios
Answer to Problem 10E
The value of trigonometric ratiosare
Explanation of Solution
Given information:
The right angle triangle with length of its sides and angles
Formula used:
The trigonometric ratios for a right angle triangle are defined as,
Calculation:
The right angle triangle with length of its sides and angles
First consider the opposite, adjacent and hypotenuse with respect to angle
Observe that opposite side is of length 4 units and hypotenuse has length 7 units.
Now, let the length of adjacent side be x , as it is a right angle triangle so,
Therefore, length of adjacent side is
Recall that the secant trigonometric ratio for a right angle triangle is defined as,
Apply it, to estimate the value of trigonometric ratios,
The value of secant function is,
Second consider the opposite, adjacent and hypotenuse with respect to angle
Observe that adjacent side is of length 4 units and hypotenuse has length 7 units.
Now, let the length of opposite side be x , as it is a right angle triangle so,
Therefore, length of opposite side is
Recall that the cosecant trigonometric ratios for a right angle triangle is defined as,
Apply it, to estimate the value of trigonometric ratios,
The value of cosecant function is,
Thus, the value of trigonometric ratiosare
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