2021 AMC 12B Problems/Problem 13
Contents
[hide]Problem
How many values of in the interval satisfy
Solution
First, move terms to get . After graphing, we find that there are solutions (two in each period of ). -dstanz5
Solution 1
We can graph two functions in this case: and . Using transformation of functions, we know that is just a cos function with amplitude 5 and frequency . Similarly, is just a sin function with amplitude 3 and shifted 1 unit downwards. So: We have solutions.
Video Solution by OmegaLearn (Using Sine and Cosine Graph)
~ pi_is_3.14
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.