Graphs of Trigonometric Functions (HSC SSCE Mathematics Advanced): Flashcards

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Graphs of Trigonometric Functions
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Coordinates of point on unit circle at angle θ\theta

(cos⁡θ,sin⁡θ)(\cos \theta, \sin \theta)

Period of y=sin⁡xy = \sin x and y=cos⁡xy = \cos x

2π2\pi

Period of y=tan⁡xy = \tan x

π\pi

Amplitude of y=sin⁡xy = \sin x and y=cos⁡xy = \cos x

11

Range of y=sin⁡xy = \sin x and y=cos⁡xy = \cos x

[−1,1][-1, 1] or −1≤y≤1-1 \leq y \leq 1

Range of y=tan⁡xy = \tan x

All real numbers or (−∞,∞)(−\infty, \infty)

Definition of tan⁡θ\tan \theta in terms of sine and cosine

tan⁡θ=sin⁡θcos⁡θ\tan \theta = \frac{\sin \theta}{\cos \theta}

Is sin⁡x\sin x an odd or even function?

Odd function: sin⁡(−x)=−sin⁡x\sin(-x) = -\sin x

Is cos⁡x\cos x an odd or even function?

Even function: cos⁡(−x)=cos⁡x\cos(-x) = \cos x

Where are the vertical asymptotes of y=tan⁡xy = \tan x?

At θ=π2+kπ\theta = \frac{\pi}{2} + k\pi, where kk is an integer

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