The Behaviour of sin x Near the Origin (HSC SSCE Mathematics Advanced): Flashcards

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The Behaviour of sin x Near the Origin
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Gradient of y=sinxy = sin x at origin

11

Tangent line to y=sinxy = sin x at origin

y=xy = x

Inequality for acute angle xx

sinx<x<anxsin x < x < an x

Inequality for - rac{pi}{2} < x < 0

sinx>x>anxsin x > x > an x

limx→0sin⁡xxlim_{x \to 0} \frac{\sin x}{x}

11

limx→0tan⁡xxlim_{x \to 0} \frac{\tan x}{x}

11

Small-angle approx for sin⁡x\sin x (radians)

sin⁡x≈x\sin x \approx x

Small-angle approx for cos⁡x\cos x (radians)

cos⁡x≈1\cos x \approx 1

Small-angle approx for tan⁡x\tan x (radians)

tan⁡x≈x\tan x \approx x

Unit required for small-angle approximations

Radians

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