12
QuizMultiple Choice

Graphing Sine and Cosine — Quiz

Question 12 • Mathematics III

Which formula gives the x -coordinates of the maximum values for y is equal to cosine of x ?

Answer
A
k pi over 2 for any positive integer k
B
k pi over 2 for k is equal to 0 comma plus or minus 2 comma plus or minus 4 comma ...
C
k pi for k is equal to 0 comma plus or minus 2 comma plus or minus 4 comma ...
D
k pi for any integer k

Explanation

The cosine function reaches its maximum value of 1 at x = 2πn, where n is any integer. Choice C gives x = kπ with k an even integer, so its values are ..., −4π, −2π, 0, 2π, 4π, ... . These are exactly the x-coordinates of the maxima.

AI-written and checked against the verified answer.

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