y = sin(x) & y = cos(x)?!?!?

Rachel

2008-07-15 8:53 am

我有以下幾條數唔係咁識做....能幫個大忙嗎?
thankyou!

請列出計算步驟和答案。定必十分感激!!

1.State the period, amplitude, max/min values, range, domain, horizontal
phase shift and vertical displacement.

a. y = - 3 cos ( 2x - 30° ) + 1

b. y = 2 cos (-1/2x + 90°) - 3

c. y = -2 sin [ 2 x ( t + 1) / 3 ]

2.The graph of y = -3sin( 2x) is shifted to the left by 30� units and up 5
units. Write the new equation.

3. Find the equation of a sine function that has a vertical displacement 2 units down, a horizontal phase shift 60° to the right, a period of 30°, a reflection in the y-axis and an amplitude of 3.

回答 (1)

用戶10012

2008-07-15 10:46 pm

✔ 最佳答案

For the function y= Asin(nx + h) + k.
A= amplitude
n = frequency, that is number of cycles in 360 degree.
Period = 1/n, that is number of degrees for one cycle.
h = phase shift . Positive is to the left, negative is to the right.
k = vertical displacement. Positive is displacing upwards, negative is displacing downwards.
domain = all real numbers for sine and cosine function.
For (a), -cos(2x -30) = cos[180 + (2x-30)] = cos(2x + 150).
So y= 3cos(2x + 150) + 1. (minus could also means reflection in the y-axis.)
Amplitude = 3, period = 360/2 = 180 degree. vertical displacement= 1, phase shift = 150 degree to the left. Max value = 3 + 1 = 4. Min value = 1-3 = -2. Range = from -2 to 4. Domain = all real values of x. You can try (b) and (c).
2.
The graph is y =-3sin(2x + 30) + 5.

2008-07-15 14:50:17 補充：
Correction: Minus could means reflection about the x -axis, not the y-axis, sorry.

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