Sketch the curve represented by the parametric equations x = 3 cos θ and y = 3 sin θ for 0≤θ≤π
http://www.wolframalpha.com/input/?i=x+%3D+3+cos+θ+and+y+%3D+3+sin+θ+for+0≤θ≤π
To sketch the curve represented by the parametric equations x = 3 cos θ and y = 3 sin θ for 0≤θ≤π, we can follow these steps:
1. Start by understanding the range of the parameter θ. In this case, θ ranges from 0 to π, which means we will be plotting points for θ values between 0 and π.
2. Next, we will create a table of values by selecting various values of θ (keeping in mind the range) and calculating the corresponding x and y values using the given parametric equations.
Let's choose a few values of θ:
- When θ = 0, x = 3 cos(0) = 3 and y = 3 sin(0) = 0. So, our first point is (3, 0).
- When θ = π/4, x = 3 cos(π/4) = 3/√2 and y = 3 sin(π/4) = 3/√2. So, our second point is approximately (2.12, 2.12).
- When θ = π/2, x = 3 cos(π/2) = 0 and y = 3 sin(π/2) = 3. So, our third point is (0, 3).
- Similarly, you can choose a few more values between 0 and π to get additional points for plotting.
3. Plot the obtained points on a graph paper. Label the points accordingly.
4. Join the plotted points with a smooth curve. This curve represents the graph of the parametric equations x = 3 cos θ and y = 3 sin θ for 0≤θ≤π.
Keep in mind that the resulting curve is a circle with a radius of 3 units, centered at the origin (0,0). You should be able to observe this when you plot the points and connect them.