Difference between revisions of "2021 AMC 12B Problems/Problem 13"
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~Jamess2022 (burntTacos) | ~Jamess2022 (burntTacos) | ||
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+ | ==Video Solution (quick, no graphing)== | ||
+ | https://youtu.be/YTn5YPQt6IY | ||
+ | ~ MathProblemSolvingSkills.com | ||
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== Video Solution by OmegaLearn (Using Sine and Cosine Graph) == | == Video Solution by OmegaLearn (Using Sine and Cosine Graph) == |
Revision as of 15:36, 16 August 2022
Contents
[hide]Problem
How many values of in the interval satisfy
Solution
We rearrange to get We can graph two functions in this case: and . Using transformation of functions, we know that is just a cosine function with amplitude and period . Similarly, is just a sine function with amplitude and shifted unit downward: So, we have solutions.
~Jamess2022 (burntTacos)
Video Solution (quick, no graphing)
https://youtu.be/YTn5YPQt6IY ~ MathProblemSolvingSkills.com
Video Solution by OmegaLearn (Using Sine and Cosine Graph)
~ pi_is_3.14
Video Solution by Hawk Math
https://www.youtube.com/watch?v=p4iCAZRUESs
See Also
2021 AMC 12B (Problems • Answer Key • Resources) | |
Preceded by Problem 12 |
Followed by Problem 14 |
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 |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.