Geometry

# Triple Angle Identities

In the above diagram, the angle between $y=ax$ and the $x$-axis is $\theta$ and the angle between $y=mx$ and the $x$-axis is $3\theta.$ If $a = \frac{1}{6},$ what is the value of $m?$

If $\sin \theta = \frac{1}{3},$ what is $\sin 3\theta?$

What is $6\times\left(\frac{3\times\tan10^{\circ}-\tan^3 10^{\circ}}{1-3\times\tan^2 10^{\circ}}\right)^2?$

If $\frac{\sin3\theta}{\cos3\theta+2\cos\theta}=7,$ what is the value of $\tan\theta?$

If $\frac{\sin3\theta}{\cos3\theta+2\cos\theta}=4,$ what is the value of $\tan\theta?$

×