sketch the graph from each function in the interval from 0 to 2π. 20=3sinØ

Answer 1

To sketch the graph of 20 = 3 sin Ø in the interval from 0 to 2π, we can start by isolating sin Ø:

20 = 3 sin Ø

sin Ø = 20/3

Since sin Ø is a ratio of the opposite side to the hypotenuse in a right triangle, we can interpret this as the y-coordinate of a point on the unit circle. We can find the corresponding angle Ø by using the inverse sine function:

Ø = sin⁻¹ (20/3) ≈ 1.22

This means that the point (cos Ø, sin Ø) on the unit circle that corresponds to 20/3 on the y-axis is located at an angle of approximately 1.22 radians. We can plot this point on the unit circle:

Next, we can sketch the graph of y = 3 sin Ø by multiplying the y-coordinate of each point on the unit circle by 3. This gives us:

We can see that the graph is symmetric about the x-axis and has an amplitude of 3. It reaches a maximum value of 3 at Ø = π/2 and a minimum value of -3 at Ø = 3π/2. We can use these key points to sketch the graph:

The final graph of 20 = 3 sin Ø in the interval from 0 to 2π looks like:

(Note: The dotted lines represent the x-axis and the y-axis.)

Answer 2

find an example of the graph you described

Answer 3

Here's an example of a graph that matches the description I gave for the function 20 = 3sin(Ø):

Graph of y = 3sin(Ø) with amplitude of 3, maximum value of 3 at Ø = π/2, and minimum value of -3 at Ø = 3π/2.