Math  /  Trigonometry

Question10. A given sinusoidal function has a period of 3 , an amplitude of 7 , and a maximum at (0(0, 2). Represent the function with a sine equation and a cosine equation. [4 marks]

Studdy Solution
The general form of a cosine function is:
y=Acos(BxC)+D y = A \cos(Bx - C) + D
Given: - Amplitude A=7 A = 7 - Period P=3 P = 3 , so B=2π3 B = \frac{2\pi}{3} - Vertical shift D=5 D = -5
Since the cosine function starts at the maximum, we can use it directly with no phase shift:
C=0 C = 0
Thus, the cosine equation is:
y=7cos(2π3x)5 y = 7 \cos\left(\frac{2\pi}{3}x\right) - 5
The sine equation representing the function is:
y=7sin(2π3x+π2)5 y = 7 \sin\left(\frac{2\pi}{3}x + \frac{\pi}{2}\right) - 5
The cosine equation representing the function is:
y=7cos(2π3x)5 y = 7 \cos\left(\frac{2\pi}{3}x\right) - 5

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