Difference between revisions of "2021 Fall AMC 12A Problems/Problem 19"
(→See Also) |
(→Problem 19) |
||
| Line 1: | Line 1: | ||
==Problem 19== | ==Problem 19== | ||
| − | Let <math>x</math> be the least real number greater than <math>1</math> such that sin<math>(x)</math> = sin<math>(x^2)</math>, where the arguments are in degrees. What is <math>x</math> rounded up to the closest integer? | + | Let <math>x</math> be the least real number greater than <math>1</math> such that \sin<math>(x)</math> = \sin<math>(x^2)</math>, where the arguments are in degrees. What is <math>x</math> rounded up to the closest integer? |
<math>\textbf{(A) } 10 \qquad \textbf{(B) } 13 \qquad \textbf{(C) } 14 \qquad \textbf{(D) } 19 \qquad \textbf{(E) } 20</math> | <math>\textbf{(A) } 10 \qquad \textbf{(B) } 13 \qquad \textbf{(C) } 14 \qquad \textbf{(D) } 19 \qquad \textbf{(E) } 20</math> | ||
Revision as of 21:21, 23 November 2021
Problem 19
Let 
be the least real number greater than 
such that \sin
= \sin
, where the arguments are in degrees. What is rounded up to the closest integer?
Solution 1
The smallest to make 
would require 
, but since needs to be greater than , these solutions are not valid.
The next smallest would require 
, or 
.
After a bit of guessing and checking, we find that 
, and 
, so the solution lies between 
and 
, making our answer 
Note: One can also solve the quadratic and estimate the radical.
~kingofpineapplz
See Also
| 2021 Fall AMC 12A (Problems • Answer Key • Resources) | |
| Preceded by Problem 18 |
Followed by Problem 20 |
| 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. 
