# The Cosine and Sine Functions

Apr 5th, 2015
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This file relates to the graphs of the cosine and sine functions. After completing the graph , the student has to answer questions on them:the domain and range of each, maximum and minimum values, period, x-and y- intercepts and the relationship between the two graphs. Answers and explanations are provided.

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The Cosine and Sine functions 1. Make a table of values for f(x) = cos (x) [more commonly written as f(x) = cos x]from -2 ? to 2 ? (plot every 1/2 ? )2. Use the table of values to sketch the graph of f(x) = cos (x) between -2 ? and 2 ?3. From your graph, answer the following questions about the Cosine functionsa. What is the Domain of f(x) = cos (x) ?b. What is the Range of f(x) = cos (x) ?c. What is the Period of f(x) = cos (x) ?d. What are the x-intercepts of f(x) = cos (x) ? e. What are the y-intercepts of f(x) = cos (x) ?f. What are the maximum and minimum values of f(x) = cos (x)?4. (a) Repeat questions 1, 2 and 3 for the sine function g(x)= sin (x) [more commonly written as g(x) = sin x](b) How are the graphs of the cosine function and sine function related to each other?Solutions1. x -2 ? -3/2 ? - ? - 1/2 ? 0 1/2 ? ? 3/2 ? 2 ? Cos (x) 1 0 -1 0 1 0 -1 0 12 cos (x)

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