Precalculus with Limits: A Graphing Approach
Precalculus with Limits: A Graphing Approach
7th Edition
ISBN: 9781305071711
Author: Ron Larson
Publisher: Brooks/Cole
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Matrices
‘Matrices’ is the plural form of the word matrix, and it is basically a spreadsheet in the form of a box. In mathematics, various functions can be carried out with matrices. Generally, a matrix comes in the shape of a square or rectangle. The elements ar…
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Chapter 5.5, Problem 97E
To determine

Tofind:Theexact value of the trigonometric function sin2α by two different methods.

Expert Solution & Answer
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Answer to Problem 97E

The exact value of the trigonometric function sin2α is 25169 .

Explanation of Solution

Given information:

The given trigonometric function is sin2α . The given diagram is as follows.

  Precalculus with Limits: A Graphing Approach, Chapter 5.5, Problem 97E

Calculation:

In the figure, the length of BC and AB is given. Calculate the hypotenuse AC.

  AC=52+122=25+144=169=13

Calculate the value of sinα .

  sinα=513

Square both the sides.

  sin2α=(513)2=25169

The value of sin2α can be calculated by Pythagoras identity.

  sin2α=1−cos2α

Calculate the value of cosα .

  cosα=1213

Substitute 1213 for cosα in the above equation.

  sin2α=1−(1213)2=1−144169=25169

From the above, it is clear that the value of sin2α is same in both the cases. Therefore, the exact value of the trigonometric function sin2α is 25169 .

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Chapter 5.5, Problem 96E
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Chapter 5.5, Problem 98E

Chapter 5 Solutions

Precalculus with Limits: A Graphing Approach

Ch. 5.1 - Prob. 1ECh. 5.1 - Prob. 2ECh. 5.1 - Prob. 3ECh. 5.1 - Prob. 4ECh. 5.1 - Prob. 5ECh. 5.1 - Prob. 6ECh. 5.1 - Prob. 7ECh. 5.1 - Prob. 8ECh. 5.1 - Prob. 9ECh. 5.1 - Prob. 10E
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