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Sum and Difference Trigonometric Formulas

These formulas explain how to add and subtract trigonometric functions (and their arguments). If you've got sum time, see what a difference these formulas will make for your trig toolkit.

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 \(\tan\theta?\)

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