Solve
R=3(1-sin theta) and graph
you can't solve it. It's just a function definition. But, the graph is at
http://www.wolframalpha.com/input/?i=r+%3D+3%281-sin%CE%B8%29
Now, if you want to see its equation in rectangular coordinates,
r = 3 - 3sinθ
r^2 = 3r - 3r sinθ
x^2+y^2 = 3r - 3x
x^2+y^2+3x = 3√(x^2+y^2)
(x^2+y^2+3x)^2 = 9(x^2+y^2)
In general, interesting and simple polar curves have nasty rectangular equations.
Well, solving equations is not really my strong suit. I'm more of a clown than a mathematician! But let me tell you a funny story instead.
Why don't scientists trust atoms?
Because they make up everything!
As for graphing the equation, I'm afraid I don't have the ability to draw graphs. But hey, you can always use a graphing calculator or online plotting tool for that!
To solve the equation R = 3(1 - sin(theta), you can follow these steps:
1. Expand the right side of the equation by distributing the 3 to both terms inside the brackets:
R = 3 - 3 sin(theta)
2. Rearrange the equation to isolate sin(theta):
3 sin(theta) = 3 - R
3. Divide both sides of the equation by 3:
sin(theta) = (3 - R) / 3
Now, to graph the equation, you can follow these steps:
1. Set up a coordinate system with theta as the x-axis and R as the y-axis.
2. Plot several points by substituting different values of theta into the equation and calculating the corresponding R values. For example, you can choose theta = 0, 30, 45, 60, 90 degrees, and so on.
3. Connect the plotted points with a smooth curve to represent the graph of the equation R = 3(1 - sin(theta)).
To solve the equation R = 3(1 - sin θ) and graph it, we will follow these steps:
Step 1: Simplify the equation.
Step 2: Create a table of values.
Step 3: Plot the points on a coordinate plane.
Step 4: Connect the points to form the graph.
Let's begin:
Step 1: Simplify the equation.
First, distribute the 3 to the terms inside the parentheses:
R = 3 - 3(sin θ)
Step 2: Create a table of values.
To graph the equation, we need to choose a set of values for θ and find the corresponding values for R.
Let's choose θ values ranging from 0 to 360 degrees (or 2π radians) in 30-degree (or π/6 radians) increments. Plug in these values into the equation and calculate the corresponding values of R.
θ | R
--------------
0° | 0
30° | 2.598
60° | 3
90° | 2.598
120° | 0
150° | -2.598
180° | -3
210° | -2.598
240° | 0
270° | 2.598
300° | 3
330° | 2.598
360° | 0
Step 3: Plot the points on a coordinate plane.
Using the values from the table, plot each point (θ, R) on a graph. The θ values will be on the x-axis, and the R values will be on the y-axis.
Step 4: Connect the points to form the graph.
Using a straight edge, draw a smooth curve connecting the plotted points. Make sure to extend the curve beyond the plotted points to show the periodic nature of the graph.
The resulting graph should be a symmetrical wave-like shape that oscillates between positive and negative values, centered around the x-axis.
Note: To graph the equation on a computer or graphing calculator, you can use the equation function and input the equation R = 3(1 - sin θ) directly.