Precalculus: Mathematics for Calculus - 6th Edition
Precalculus: Mathematics for Calculus - 6th Edition
6th Edition
ISBN: 9780840068071
Author: Stewart, James, Redlin, Lothar, Watson, Saleem
Publisher: Cengage Learning
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Fundamentals of Trigonometric Identities
Trigonometric Identities are the equalities that involve trigonometry functions and hold for all the values of variables given in the equation.
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Chapter 5.1, Problem 37E
To determine

To find: the reference number for each value of angle t.

Expert Solution & Answer
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Answer to Problem 37E

  (a)t¯=2π7 , (b)t¯=2π9 , (c)t¯=0.142 and (d)t¯=1.283 .

Explanation of Solution

Given:

  (a)t=5π7 . (b)t=−7π9 .

  (c)t=-3 . (d)t=5 .

Concept used:

For a unit circle:

  r=1 .

  x=cosθ .

  y=sinθ .

The reference angle should be less than π2 .

The angle is always considered or calculated form x-axis.

Due to periodic nature of sine and cosine function the value of the angle repeat again and again therefore the higher value of angle can be interprets in-term of reference angle which is less than 900 .

Calculation:

  (a)t=5π7

Which can be written as:

  t=5π7=π-2π7=2π7 .

Since during horizontal shift trigonometric ratio did not change and its reference angle will be generated.

  T(π-θ)=T(θ) .

Let T be any trigonometric ratio and irrespective of trigonometric all give same reference angle.

Therefore

  (a)t¯=2π7 .

Likewise,

  (b)−7π9 .

Which can be written as:

  t=-7π9=π-2π9=2π9 .

Since during horizontal shift trigonometric ratio did not change and its reference angle will be generated.

Therefore,

  (b)t¯=2π9 .

Likewise,

  (c)t=-3 .

Which can be written as:

  t=-3=π-3=0.142 .

Therefore,

  (c)t¯=0.142 .

Since during horizontal shift trigonometric ratio did not change and its reference angle will be generated.

  (d)t=5

Which can be written as:

  t=5=2π-5=1.283 .

Since the angle lies in 1st quadrant the angle its reference angle

Therefore,

  (d)t¯=1.283 .

Hence, (a)t¯=2π7 , (b)t¯=2π9 , (c)t¯=0.142 and (d)t¯=1.283 .

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Chapter 5.1, Problem 36E
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Chapter 5.1, Problem 38E

Chapter 5 Solutions

Precalculus: Mathematics for Calculus - 6th Edition

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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Electric Generator The graph shows an oscilloscope...Ch. 5.6 - Doppler Effect When a car with its horn blowing...Ch. 5.6 - Motion of a Building A strong gust of wind strikes...Ch. 5.6 - Shock Absorber When a car hits a certain bump on...Ch. 5.6 - Tuning Fork A tuning fork is struck and oscillates...Ch. 5.6 - Guitar String A guitar string is pulled at point P...Ch. 5 - Prob. 1RCCCh. 5 - Prob. 2RCCCh. 5 - Prob. 3RCCCh. 5 - Prob. 4RCCCh. 5 - Prob. 5RCCCh. 5 - Prob. 6RCCCh. 5 - Prob. 7RCCCh. 5 - Prob. 8RCCCh. 5 - Prob. 9RCCCh. 5 - Prob. 10RCCCh. 5 - Prob. 11RCCCh. 5 - Prob. 12RCCCh. 5 - Prob. 1RECh. 5 - Prob. 2RECh. 5 - Prob. 3RECh. 5 - Prob. 4RECh. 5 - Prob. 5RECh. 5 - Prob. 6RECh. 5 - Prob. 7RECh. 5 - Prob. 8RECh. 5 - Prob. 9RECh. 5 - Prob. 10RECh. 5 - Prob. 11RECh. 5 - Prob. 12RECh. 5 - Prob. 13RECh. 5 - Prob. 14RECh. 5 - Prob. 15RECh. 5 - Prob. 16RECh. 5 - Prob. 17RECh. 5 - Prob. 18RECh. 5 - Prob. 19RECh. 5 - Prob. 20RECh. 5 - Prob. 21RECh. 5 - Prob. 22RECh. 5 - Prob. 23RECh. 5 - Prob. 24RECh. 5 - 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