Geometry

Sum and Difference Trigonometric Formulas

三倍角的身份

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

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

What is 6 × ( 3 × tan 1 0 tan 3 1 0 1 3 × tan 2 1 0 ) 2 ? 6\times\left(\frac{3\times\tan10^{\circ}-\tan^3 10^{\circ}}{1-3\times\tan^2 10^{\circ}}\right)^2?

If sin 3 θ cos 3 θ + 2 cos θ = 7 , \frac{\sin3\theta}{\cos3\theta+2\cos\theta}=7, what is the value of tan θ ? \tan\theta?

If sin 3 θ cos 3 θ + 2 cos θ = 4 , \frac{\sin3\theta}{\cos3\theta+2\cos\theta}=4, what is the value of tan θ ? \tan\theta?

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