Difference between revisions of "2021 AMC 12B Problems/Problem 13"
(Created page with "==Problem== How many values of <math>\theta</math> in the interval <math>0<\theta\le 2\pi</math> satisfy<cmath>1-3\sin\theta+5\cos3\theta?</cmath><math>\textbf{(A) }2 \qquad \...") |
(→Solution) |
||
| Line 4: | Line 4: | ||
==Solution== | ==Solution== | ||
{{solution}} | {{solution}} | ||
| + | |||
| + | First, move terms to get <math>1+5cos3x=3sinx</math>. After graphing, we find that there are <math>\boxed{6}</math> solutions. (two in each period of <math>5cos3x</math>) | ||
==See Also== | ==See Also== | ||
{{AMC12 box|year=2021|ab=B|num-b=12|num-a=14}} | {{AMC12 box|year=2021|ab=B|num-b=12|num-a=14}} | ||
{{MAA Notice}} | {{MAA Notice}} | ||
Revision as of 22:49, 11 February 2021
Problem
How many values of 
in the interval 
satisfy![\[1-3\sin\theta+5\cos3\theta?\]](http://latex.artofproblemsolving.com/c/2/4/c24b458f389d63f407e3740dc64386119db8a8c3.png)
Solution
This problem needs a solution. If you have a solution for it, please help us out by adding it.
First, move terms to get 
. After graphing, we find that there are 
solutions. (two in each period of 
)
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. 
