Difference between revisions of "2020 AMC 12A Problems/Problem 9"

Revision as of 16:15, 1 February 2020

How many solutions does the equation tan $(2x)=cos(\frac{x}{2})$ have on the interval $[0,2\pi]?$

$\textbf{(A)}\ 1\qquad\textbf{(B)}\ 2\qquad\textbf{(C)}\ 3\qquad\textbf{(D)}\ 4\qquad\textbf{(E)}\ 5$

Draw a graph of tan $(2x)$ and $cos(\frac{x}{2})$

tan $(2x)$ has a period of $\frac{\pi}{2}$ and asymptotes at $\frac{\pi}{4}+\frac{k\pi}{2}$ .

$cos(\frac{x}{2})$ has a period of $4\pi$ and zeroes at $\pi$ .

Drawing such a graph would get $\boxed{\textbf{E) }5}$ ~lopkiloinm

2020 AMC 12A (Problems • Answer Key • Resources)
Preceded by Problem 8	Followed by Problem 10
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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 ==See Also==
-{{AMC12 box|year=2020|ab=A|num-b=1|num-a=3}}
+{{AMC12 box|year=2020|ab=A|num-b=8|num-a=10}}
 {{MAA Notice}}