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Concept explainers
The Sawtooth Curve An oscilloscope often displays a sawtooth curve. This curve can be approximated by sinusoidal curves of varying periods and amplitudes.
(a) Use a graphing utility to graph the following function, which can be used to approximate the sawtooth curve.(a) Use a graphing utility to graph the following function, which can be used to approximate the sawtooth curve.
(b) A better approximation to the sawtooth curve is given by
Use a graphing utility to graph this function for and compare the result to the graph obtained in part (a).
(c) A third and even better approximation to the sawtooth curve is given by
Use a graphing utility to graph this function for and compare the result t
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Chapter 8 Solutions
Precalculus
Additional Math Textbook Solutions
Calculus, Single Variable: Early Transcendentals (3rd Edition)
University Calculus: Early Transcendentals (4th Edition)
Glencoe Math Accelerated, Student Edition
Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (4th Edition)
Single Variable Calculus: Early Transcendentals (2nd Edition) - Standalone book
- Biorhythms A popular theory that attempts to explain the ups and downs of everyday life states that each person has three cycles, called biorhythms, which begin at birth. These three cycles can be modeled by the sine functions below, where t is the number of days since birth. Physical (23 days): P=sin2t23,t0 Emotional (28 days): E=sin2t28,t0 Intellectual (33 days): I=sin2t33,t0 Consider a person who was born on July 20,1995. (a) Use a graphing utility to graph the three models in the same viewing window for 7300t7380. (b) Describe the person’s biorhythms during the month of September 2015. (c) Calculate the person’s three energy levels on September 22,2015.arrow_forwardFor a function to have an inverse, it must be ___________. To define the inverse sine function, we restrict the ____________ of the sine function to the interval ____________.arrow_forwardThe origins of the sine function are found in the tables of chords for a circle constructed by the Greek astronomers/mathematicians Hipparchus and Ptolemy. However, the origins of the tangent and cotangent functions lie primarily with Arabic and Islamic astronomers. Called the umbra recta and umbra versa, their connection was not to the chord of a circle but to the gnomon of a sundial. Research the origins of the tangent and cotangent functions. What was the connection to sundials? What other contributions did Arabic astronomers make to trigonometry? Write a paragraph or two about your findings.arrow_forward
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