1. Write an equation of the following using the particular function.
1. The function is sine. The amp is 2 and the domain is [0, 2].
I got y=2sin(pie(x))
but i plugged that in my calc and it doesnt look like the graph on my worksheet
2. The function is cosine. The amp is 3 and the domain is [-pie/3, 11pie/3]
I got y=3cos(3/5x-pie)
thanks!!
To write the equation of the given functions using the particular function, let's go through the steps for each case:
1. For the sine function with an amplitude of 2 and a domain of [0, 2], the equation can be written as:
y = A*sin(Bx)
where A is the amplitude and B determines the period. In this case, A = 2, so the equation becomes:
y = 2*sin(Bx)
To determine the value of B, we need to find the period of the sine function. The period of the sine function is given by the formula: period = 2π/B. In this case, the domain is [0, 2], which corresponds to one full period of the sine function. Therefore, the period is 2, and we can set up the equation:
2 = 2π/B
Solving for B, we get:
B = π
So the equation becomes:
y = 2*sin(πx)
Make sure to double-check your calculator settings for the degree/radian mode as it can affect the appearance of the graph.
2. For the cosine function with an amplitude of 3 and a domain of [-π/3, 11π/3], the equation can be written as:
y = A*cos(Bx)
where A is the amplitude and B determines the period. In this case, A = 3, so the equation becomes:
y = 3*cos(Bx)
To find the value of B, we need to determine the period. The period of the cosine function is given by the formula: period = 2π/B. In this case, the domain is [-π/3, 11π/3], which corresponds to four full periods of the cosine function. Therefore, the period is 4, and we can set up the equation:
4 = 2π/B
Solving for B, we get:
B = π/2
So the equation becomes:
y = 3*cos(π/2 * x)
Keep in mind that when calculating the coefficient of x, it should be multiplied by the whole term inside the cosine function. Therefore, the correct equation is:
y = 3*cos(π/2 * x)
Remember to check your calculator settings for the degree/radian mode while graphing the function as well.
I hope this explanation helps you understand how to write the equations of sine and cosine functions using the given amplitude and domain.