y = 4 cos (3/4) θ
a. amplitude = 4
b. number of cycles = ?
c. period = (8pi/3)
for cos kx, you will have k complete cycles from 0 to 2π , so .....
check:
http://www.wolframalpha.com/input/?i=plot+y+%3D+4+cos+(3x%2F4)
So there will be a cycle for every curve?
A cycle is one completed curve of the cosine curve, or any other cyclic curve.
Usually in questions like this, it might ask "how many cycles are there for the given curve in the interval from 0 to 360° or 2π radians.
in your case the graph I gave you shows that from 0 to 2π, there would be 3/4 of a complete cycle. Notice that agrees with the property I stated above.
To answer these questions about the equation y = 4 cos(3/4)θ, let's break down the equation and the properties of a cosine function.
1. Amplitude:
The amplitude of a cosine function is the absolute value of the coefficient in front of the cosine term. In this equation, the coefficient is 4, so the amplitude is simply 4.
Answer: a. The amplitude is 4.
2. Number of cycles:
The number of cycles refers to the number of complete oscillations or repetitions of the cosine function. To determine the number of cycles based on the equation, we need to find the period.
3. Period:
The period of a cosine function is determined by the coefficient in front of the angle (θ). In this equation, the coefficient is (3/4). The general formula for the period of a cosine function is 2π divided by the coefficient, so the period in this case is (2π) / (3/4), which simplifies to (8π/3).
Answer: c. The period is (8π/3).
To find the number of cycles within the given period, we need to divide the total period by the individual period of one complete cycle. In this case, the individual period of one complete cycle is equal to the overall period.
So, to find the number of cycles:
Number of cycles = Total period / Individual period
Number of cycles = (8π/3) / (8π/3)
Number of cycles = 1
Answer: b. The number of cycles is 1.