The Cosine Function (Grade 11 NSC Matric Mathematics): Flashcards

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The Cosine Function
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Period of y=cos⁡θy = \cos θ

360°360°

Amplitude of y=cos⁡θy = \cos θ

11

Range of y=cos⁡θy = \cos θ

[−1;1][-1; 1]

Y-intercept of y=cos⁡θy = \cos θ

(0°;1)(0°; 1) - starts at maximum value

Period formula for y=cos⁡(kθ)y = \cos(kθ)

360°∣k∣\frac{360°}{|k|}

Effect of parameter qq in y=acos⁡θ+qy = a\cos θ + q

Vertical shift: up if q>0q > 0, down if q<0q < 0

Effect of parameter aa in y=acos⁡θy = a\cos θ

Changes amplitude to ∣a∣|a|; reflects if a<0a < 0

Range of y=acos⁡θ+qy = a\cos θ + q

[q−∣a∣;q+∣a∣][q - |a|; q + |a|]

Phase shift for p>0p > 0 in y=cos⁡(θ+p)y = \cos(θ + p)

Shifts left by pp degrees

Even function property of cosine

cos⁡(−θ)=cos⁡θ\cos(-θ) = \cos θ

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