Sum and Difference Trigonometric Formulas

Triple Angle Identities


In the above diagram, the angle between y=axy=ax and the xx-axis is θ\theta and the angle between y=mxy=mx and the xx-axis is 3θ.3\theta. If a=16,a = \frac{1}{6}, what is the value of m?m?

If sinθ=13,\sin \theta = \frac{1}{3}, what is sin3θ?\sin 3\theta?

What is 6×(3×tan10tan31013×tan210)2?6\times\left(\frac{3\times\tan10^{\circ}-\tan^3 10^{\circ}}{1-3\times\tan^2 10^{\circ}}\right)^2?

If sin3θcos3θ+2cosθ=7,\frac{\sin3\theta}{\cos3\theta+2\cos\theta}=7, what is the value of tanθ?\tan\theta?

If sin3θcos3θ+2cosθ=4,\frac{\sin3\theta}{\cos3\theta+2\cos\theta}=4, what is the value of tanθ?\tan\theta?


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