The Tangent Function (VCE SSCE Mathematical Methods): Flashcards

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The Tangent Function
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Definition of tanθ\tan \theta in terms of sine and cosine

tanθ=sinθcosθ\tan \theta = \frac{\sin \theta}{\cos \theta}

Period of basic tangent function y=tanθy = \tan \theta

π\pi units

Range of the tangent function

All real numbers (R\mathbb{R})

Vertical asymptotes location for y=tanθy = \tan \theta

θ=(2k+1)π2\theta = \frac{(2k+1)\pi}{2} (odd multiples of π2\frac{\pi}{2})

Axis intercepts for y=tanθy = \tan \theta

θ=kπ\theta = k\pi (integer multiples of π\pi)

Period of y=atan(nt)y = a \tan(nt)

πn\frac{\pi}{n}

Exact value of tan(π4)\tan\left(\frac{\pi}{4}\right)

11

Exact value of tan(π3)\tan\left(\frac{\pi}{3}\right)

3\sqrt{3}

Odd function property of tangent

tan(θ)=tanθ\tan(-\theta) = -\tan \theta

How to solve sin(nx)=kcos(nx)\sin(nx) = k \cos(nx)

Convert to tan(nx)=k\tan(nx) = k

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