2021 AMC 12B Problems/Problem 13

Problem

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

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

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

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2021 AMC 12B Problems/Problem 13

Contents

Problem

Solution

Video Solution by OmegaLearn (Using Sine and Cosine Graph)

See Also