# Difference between revisions of "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

~ pi_is_3.14