Cos2x and 3Sin2x

We have two graphs, one for f(x)=Cos2x and another for g(x)=3Sin2x

for both of them being between 0 - 180 deg.

The question is: Calculate the values for x where f(x) = g(x) if x $\in$ (0;180)

Hello juriemagic!

$f(x)=g(x)\\ cos\ 2x=3sin\ 2x$

$u=2x$

$cos\ u=3sin\ u\\ cos^2\ u =3(1-cos^2\ u)\\ cos^2\ u=3-3cos^2\ u\\ 4cos^2\ u=3\\ cos\ u=\sqrt{\frac{3}{4}}=\frac{\sqrt{3}}{2}$

$u=30^{\circ}\\ x=\frac{u}{2}$

$x=15^{\circ}$

  !

We have two graphs, one for f(x)=Cos2x and another for g(x)=3Sin2x

for both of them being between 0 - 180 deg.

The question is: Calculate the values for x where f(x) = g(x) if x $\in$ (0;180)

Hello juriemagic!            Answer 1 # is wrong!

$f(x)=g(x)\\ cos\ 2x=3sin\ 2x$

$u=2x$

$cos\ u=3sin\ u\\ cos^2\ u =9(1-cos^2\ u)\\ cos^2\ u=9-9cos^2\\ 10cos^2\ u=9\\ cos\ u=\pm\sqrt{\frac{9}{10}}=\pm \frac{3}{\sqrt{10}}$

$u_1=18.435^{\circ}\\ u_2=161.565^{\circ}$

$x=\frac{u}{2}$

$x_1=9.217^{\circ}\\ x_2=80.783^{\circ}$

  !