Difference between revisions of "2021 AMC 12B Problems/Problem 13"
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==Problem== | ==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 \textbf{(B) }4 \qquad \textbf{(C) }5\qquad \textbf{(D) }6 \qquad \textbf{(E) }8</math> | + | 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 = 0?</cmath><math>\textbf{(A) }2 \qquad \textbf{(B) }4 \qquad \textbf{(C) }5\qquad \textbf{(D) }6 \qquad \textbf{(E) }8</math> |
==Solution== | ==Solution== | ||
Revision as of 01:52, 12 February 2021
Contents
Problem
How many values of 
in the interval 
satisfy![\[1-3\sin\theta+5\cos3\theta = 0?\]](http://latex.artofproblemsolving.com/b/5/8/b58210a8828d746350c9d6235739f48869ca7cf6.png)
Solution
First, move terms to get 
. After graphing, we find that there are 
solutions (two in each period of 
). -dstanz5
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 | |
These problems are copyrighted © by the Mathematical Association of America, as part of the American Mathematics Competitions. 
