i need to graph the polar equation
2 = r cos (theta + 180) on one of the graphs that looks like a flattened globe.
So far I have
2=r cos180 costheta + r sin180 sintheta
what do i do now?
Isn't cos(Theta+180)= -cosTheta ?
checking the hard way...
cos(A+B)=cosAcosB-sinAsinB
cos(Theta+180)= cosThetacos180-sinThetasin180= -cosTheta.
2= -rcosTheta
r= -2/cosTheta.
Graph it.
thank you so much, I don't know how i missed that identity.
To graph the polar equation 2 = r cos (theta + 180), you can simplify the equation further:
Using the identities cos (theta + 180) = -cos(theta) and sin (theta + 180) = -sin(theta), the equation becomes:
2 = -r cos(theta)
Now, you can rearrange the equation to solve for r:
r = -2 / cos(theta)
To graph this equation, you can follow these steps:
1. Choose a range of values for theta. For example, you can start with theta ranging from 0 to 360 degrees or 0 to 2π radians.
2. Calculate the corresponding values of r for each theta using the equation r = -2 / cos(theta).
3. Plot the points (r, theta) on a polar coordinate graph. The distance from the origin represents the value of r, and the angle from the positive x-axis represents theta.
4. Connect the plotted points to form a continuous curve.
The graph of the polar equation 2 = r cos (theta + 180) on a polar coordinate system resembling a flattened globe should resemble an inverted circle centered at the origin.