Multiple Choice
Sketch the function on the graph below.
10. Graphing Trigonometric Functions
Graphs of the Sine and Cosine Functions
Multiple Choice
The Period for the function is . Determine the correct value of b.
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Verified step by step guidance1
Understand that the period of a cosine function y = cos(bx) is given by the formula T = \(\frac{2\pi}{b}\).
Set the given period T = 20\(\pi\) equal to the formula for the period: \(\frac{2\pi}{b}\) = 20\(\pi\).
To solve for b, first isolate b by multiplying both sides of the equation by b: 2\(\pi\) = 20\(\pi\) \(\cdot\) b.
Divide both sides of the equation by 20\(\pi\) to solve for b: b = \(\frac{2\pi}{20\pi}\).
Simplify the expression \(\frac{2\pi}{20\pi}\) by canceling \(\pi\) from the numerator and the denominator, resulting in b = \(\frac{1}{10}\).
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