Difference between revisions of "2021 AMC 12B Problems/Problem 13"

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==Solution==
 
==Solution==
  
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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>). -dstanz5
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== Video Solution by OmegaLearn (Using Sine and Cosine Graph) ==
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https://youtu.be/toBOpc6vS6s
  
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>). -dstanz5
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~ pi_is_3.14
  
 
==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 21:54, 11 February 2021

Problem

How many values of $\theta$ in the interval $0<\theta\le 2\pi$ satisfy\[1-3\sin\theta+5\cos3\theta?\]$\textbf{(A) }2 \qquad \textbf{(B) }4 \qquad \textbf{(C) }5\qquad \textbf{(D) }6 \qquad \textbf{(E) }8$

Solution

First, move terms to get $1+5cos3x=3sinx$. After graphing, we find that there are $\boxed{6}$ solutions (two in each period of $5cos3x$). -dstanz5


Video Solution by OmegaLearn (Using Sine and Cosine Graph)

https://youtu.be/toBOpc6vS6s

~ pi_is_3.14

See Also

2021 AMC 12B (ProblemsAnswer KeyResources)
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

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