Trigonometric Functions (AQA A-Level Mathematics): Flashcards

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Transformations of Trigonometric Functions
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Vertical stretch/reflection form for trig functions

y=Asin⁡(x)y = A\sin(x), y=Acos⁡(x)y = A\cos(x), or y=Atan⁡(x)y = A\tan(x)

Effect when ∣A∣>1|A| > 1 in y=Asin⁡(x)y = A\sin(x)

Graph is stretched vertically

Effect when A<0A < 0 in trig function y=Asin⁡(x)y = A\sin(x)

Graph is reflected across the xx-axis

Horizontal stretch/compression form for trig functions

y=sin⁡(Bx)y = \sin(Bx), y=cos⁡(Bx)y = \cos(Bx), or y=tan⁡(Bx)y = \tan(Bx)

Period of y=sin⁡(Bx)y = \sin(Bx) or y=cos⁡(Bx)y = \cos(Bx)

360°∣B∣\frac{360°}{|B|} or 2π∣B∣\frac{2\pi}{|B|}

Period of y=tan⁡(Bx)y = \tan(Bx)

180°∣B∣\frac{180°}{|B|} or π∣B∣\frac{\pi}{|B|}

Effect of C>0C > 0 in y=sin⁡(x)+Cy = \sin(x) + C

Graph shifts up by CC units

Effect of D>0D > 0 in y=sin⁡(x−D)y = \sin(x - D)

Graph shifts to the right by DD units

Effect of D<0D < 0 in y=sin⁡(x−D)y = \sin(x - D)

Graph shifts to the left by ∣D∣|D| units

Effect when ∣B∣>1|B| > 1 in y=sin⁡(Bx)y = \sin(Bx)

Graph compressed horizontally (period decreases)

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