determine the amplitude and period of each function.
1) y = 3sin (2x-pi/2)
2) y = -3sin2 (x-pi/4)
3) y = 2cos (2x+pi)
4) y = -2cos2 (x+pi/2)
for y = a sin (kx) or y = a cos (kx)
the amplitude is |a| and the period is 2π/k
so for the first one, y = 3 sin (2x - π/2)
amplitude is 3 , period = 2π/2 = π
do the others the same way.
The amplitude is the coefficient in front of the trig term. Forget whether it is + or -.
Let a be the number in front of the x.
a = 2 pi/P, so
P = 2 pi/a
For question 1), the amplitude is 3 and the period is pi
To determine the amplitude and period of each function, we can use the standard form of a trigonometric function:
1) For y = 3sin(2x-pi/2):
Amplitude: The amplitude of a sine function is equal to the absolute value of the coefficient in front of the sine term. In this case, the amplitude is 3.
Period: The period of a sine function is given by 2π divided by the coefficient of x. In this case, the period is 2π/2 = π.
2) For y = -3sin2(x-pi/4):
Amplitude: The amplitude in this case is -3 since the negative sign affects the entire function.
Period: The period is determined by 2π divided by the coefficient of x, which is 2. Therefore, the period is 2π/2 = π.
3) For y = 2cos(2x+pi):
Amplitude: The amplitude of a cosine function is equal to the absolute value of the coefficient in front of the cosine term. In this case, the amplitude is 2.
Period: The period is determined by 2π divided by the coefficient of x, which is 2. Therefore, the period is 2π/2 = π.
4) For y = -2cos2(x+pi/2):
Amplitude: The amplitude in this case is -2 since the negative sign affects the entire function.
Period: The period is determined by 2π divided by the coefficient of x, which is 2. Therefore, the period is 2π/2 = π.
To summarize:
1) Amplitude = 3, Period = π.
2) Amplitude = -3, Period = π.
3) Amplitude = 2, Period = π.
4) Amplitude = -2, Period = π.
To determine the amplitude and period of each function, we need to understand the general form of a sinusoidal function:
y = A * sin(Bx + C)
1) For y = 3sin(2x - pi/2):
Amplitude (A): The amplitude of a sinusoidal function is the absolute value of the coefficient outside the sine function. In this case, the amplitude is |3| = 3.
Period: The period of a sinusoidal function is given by 2π/B. In this case, B = 2, so the period is 2π/2 = π.
Therefore, the amplitude of the function is 3, and the period is π.
2) For y = -3sin^2(x - pi/4):
Amplitude (A): In this case, there is a square function inside the sine function. The square function does not change the amplitude, so the amplitude is also 3.
Period: Similar to before, the period is given by 2π/B. Here, B = 1, so the period is 2π/1 = 2π.
The amplitude is 3, and the period is 2π.
3) For y = 2cos(2x + pi):
Amplitude (A): The amplitude of a cosine function is the absolute value of the coefficient outside the cosine function. In this case, the amplitude is |2| = 2.
Period: Like before, the period is given by 2π/B. Here, B = 2, so the period is 2π/2 = π.
So, the amplitude is 2, and the period is π.
4) For y = -2cos^2(x + pi/2):
Amplitude (A): Similar to the second function, there is a square function inside the cosine function, which does not change the amplitude. Thus, the amplitude is 2.
Period: The period is given by 2π/B. Here, B = 1, so the period is 2π/1 = 2π.
Hence, the amplitude is 2, and the period is 2π.