I have to graph the following:
2 = rcos(theta-20 degrees). I put it in the form r = 2/cos(theta-20degrees). Is this correct? I am having trouble with my table of values.
I would appreciate your help. Thanks.
Yes that is OK. It looks like this will simplify to the equation for a straight line that is perpendicular to the line theta = 20 degrees and goes through r = 2, theta = 20 (x = 1.879, y = 0.684)
Expand the cosine function to
cos theta cos 20 + sin theta sin 20
and you have
2 = x cos 20 + y sin 20
which is the equation of a straight line.
Thank you for helping.
To graph the equation 2 = rcos(θ-20 degrees), you're on the right track by converting it to the polar form r = 2/cos(θ-20 degrees). This form will help you determine the values of r for different angles(θ) at which you can plot points.
Now, to create a table of values, you can choose different values for θ and calculate the corresponding values for r using the equation r = 2/cos(θ-20 degrees). Here's how you can proceed:
1. Choose a range of values for θ, such as -180 degrees to 180 degrees.
2. Increment θ in a suitable interval, such as 10 degrees or 15 degrees.
3. For each value of θ, substitute it into the equation r = 2/cos(θ-20 degrees) to calculate the corresponding value of r.
4. Tabulate the values of θ and r in a table.
Once you have the table of values, you can plot the points (r,θ) on a polar coordinate system. Remember that the angle θ represents the direction of the point from the origin, and r represents the distance of the point from the origin.
If you're experiencing trouble creating the table of values or plotting the points, please let me know the specific difficulties you're facing, and I'll be glad to help you further.