Difference between revisions of "2017 AMC 12B Problems/Problem 7"
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The functions <math>\sin(x)</math> and <math>\cos(x)</math> are periodic with least period <math>2\pi</math>. What is the least period of the function <math>\cos(\sin(x))</math>? | The functions <math>\sin(x)</math> and <math>\cos(x)</math> are periodic with least period <math>2\pi</math>. What is the least period of the function <math>\cos(\sin(x))</math>? | ||
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==Solution== | ==Solution== | ||
| + | Start by noting that <math>\cos(-x)=\cos(x)</math>. Then realize that under this function, the negative sine values yield the same as their positive value, so take the absolute value of the sine function to get the new period. This has period <math>\pi</math>, so the answer is <math>\boxed{(B)}</math>. | ||
==See Also== | ==See Also== | ||
{{AMC12 box|year=2017|ab=B|num-b=6|num-a=8}} | {{AMC12 box|year=2017|ab=B|num-b=6|num-a=8}} | ||
{{MAA Notice}} | {{MAA Notice}} | ||
| + | |||
| + | [[Category:Introductory Trigonometry Problems]] | ||
Revision as of 22:36, 26 October 2021
Problem
The functions 
and 
are periodic with least period 
. What is the least period of the function 
?
The function is not periodic.
Solution
Start by noting that 
. Then realize that under this function, the negative sine values yield the same as their positive value, so take the absolute value of the sine function to get the new period. This has period 
, so the answer is 
.
See Also
| 2017 AMC 12B (Problems • Answer Key • Resources) | |
| Preceded by Problem 6 |
Followed by Problem 8 |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | |
| All AMC 12 Problems and Solutions | |
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