1.
What is the horizontal length required to complete one cycle called?
Correct Answer
B. Period
Explanation
The horizontal length required to complete one cycle is called the period. The period represents the time it takes for a complete oscillation or vibration to occur. It is often measured in seconds and is a fundamental concept in the study of waves and oscillations. The period is inversely related to the frequency of the wave, meaning that a shorter period corresponds to a higher frequency and vice versa.
2.
Which value represents amplitude in the function y = a sin(bx-h) + k
Correct Answer
A. A
Explanation
The value "a" represents the amplitude in the function y = a sin(bx-h) + k. Amplitude refers to the maximum displacement or distance from the equilibrium position in a periodic function. In this case, "a" determines the vertical stretch or compression of the graph, indicating how high or low the function will oscillate from the midline.
3.
The __________ measure the distance from the midline to the max or min of the function.
Correct Answer
C. Amplitude
Explanation
The amplitude of a function measures the distance from the midline (or average value) of the function to its maximum or minimum value. It represents the maximum displacement of the function from its midline.
4.
If no dilations occur, what is the normal period of a sine or cosine function?
Correct Answer
A. 2π
Explanation
The normal period of a sine or cosine function is 2π. This means that the graph of the function repeats itself every 2π units along the x-axis.
5.
What is the amplitude of y=3sin(7x)-2?
Correct Answer
B. 3
Explanation
The amplitude of a sine function is the distance between the maximum and minimum values of the function. In this case, the coefficient in front of the sine function is 3, which represents the amplitude. Therefore, the amplitude of y=3sin(7x)-2 is 3.
6.
The period of a sine or cosine graph can be found by
Correct Answer
D. 2π/B
Explanation
The period of a sine or cosine graph can be found by dividing 2π by the coefficient of the variable inside the trigonometric function. In this case, the coefficient is B, so the period would be 2π/B.
7.
What is the amplitude and period of y = 2sin(πx)?
Correct Answer
C. 2 and 2
Explanation
The given equation is in the form y = A*sin(Bx), where A represents the amplitude and B represents the period. In this case, the amplitude is 2, which represents the maximum value that the function reaches above and below the x-axis. The period is also 2, which represents the distance between two consecutive peaks or troughs of the graph.
8.
Find the amplitude and period f(x)= 2sinx.
Correct Answer
A. A = 2, P = 2π
Explanation
The amplitude of a sinusoidal function determines the maximum distance the graph reaches from its midline. In this case, the amplitude is 2, indicating that the graph oscillates between a maximum value of 2 and a minimum value of -2.
The period of a sinusoidal function is the distance between two consecutive peaks or troughs of the graph. In this case, the period is 2π, which means that the graph completes one full cycle every 2π units.
Therefore, the correct answer is A = 2, P = 2π.
9.
Write the equation for a sine function with an amplitude of 6 and a period of π/4.
Correct Answer
B. Y=6sin(8x)
Explanation
The equation for a sine function with an amplitude of 6 and a period of π/4 is y=6sin(8x). The amplitude of 6 means that the graph will oscillate between -6 and 6. The period of π/4 means that the graph will complete one full cycle in a distance of π/4 on the x-axis. The coefficient of 8 in front of x indicates that the graph will be compressed horizontally, making it oscillate more rapidly.
10.
Convert 100⁰ to radians.
Correct Answer
D. 5π/9
Explanation
To convert degrees to radians, we use the formula: radians = (degrees * π) / 180. In this case, we have 100 degrees. Plugging this value into the formula, we get: radians = (100 * π) / 180 = 5π/9. Therefore, the correct answer is 5π/9.