Question

The sound wave of two music notes can be represented by the function y = -2cos2x and y = cos2x, where x represents the time since the note is played. At what times will the frequencies of the sound waves be the same in the interval [0°, 360°)?

A. x = 0º, 180º, 270º, 300º

B. x = 60º, 120º, 240º, 300º

C. x = 0º, 60º, 120º, 180º

D. x = 60º, 100º, 140º, 180º

Answer 1

Okay I was thinking A.) as my answer am I correct?

Answer 2

@surjithayer

Answer 3

\[-2\cos 2x=\cos 2x\]
\[\cos 2x+2\cos 2x=0\]\[3\cos 2x=0\]
\[\cos 2x=0=\cos (2n+1)90\]
\[2x=(2n+1)90\]
x=45(2n+1)
\[n \in I\]
n=0
\[x=45^\circ\]
n=1
\[x=135^\circ \]
n=2
\[x=225^\circ\]
n=3
\[x=315^\circ\]
n=4
\[x=405^\circ\]
Rejected
there is something wrong either in my calculation or in statement.

Answer 4

Hmm okay so what did you get as your answer?

Answer 5

@surjithayer

Answer 6

whether it is \[y=-2 cos2x\]
or
\[y=-2 cos^2x\]
similarly for second equation.

Answer 7

if
\[y=-2\cos ^2x \]
and
\[y=\cos 2x=\cos ^2x-\sin ^2x\]
\[-2\cos ^2x=\cos ^2x-\sin ^2x\]
\[\sin ^2x=3\cos ^2x\]
\[2\sin ^2x=3(2\cos ^2x)\]
\[1-\cos 2x=3(1+\cos 2x)\]
\[1-\cos 2x=3+3\cos 2x\]
\[4\cos 2x=-2\]
\[\cos 2x=-\frac{ 1 }{ 2 }=-\cos 60\]\[=\cos (180-60),\cos (180+60),\cos(360+180-60),\cos(360+180+60)\]
2x=120,240,480,600
x=60,120,240,300
so B
in future post correct statement.