Given r = 10 cos θ
If you sketched an angle of θ = 150 degrees, what quadrant would it be located in?
It's either the first or second... I think second?
Multiply both sides of r = 10 cos θ by r. Transform the resulting equation into Cartesian coordinates.
second is from 90 to 180 degrees
r^2 = 100 cos^2 T
x^2 + y^2 = 100 [ x^2/(x^2+y^2) ]
(x^2 + y^2)^2 =100 x^2
x^4 + 2 x^2 y^2 + y^4 = 100 x^2
Thank you so much!
To determine the quadrant in which the angle θ = 150 degrees is located, we can use the following guidelines:
1. Recall that the first quadrant ranges from 0 to 90 degrees.
2. The second quadrant ranges from 90 to 180 degrees.
3. The third quadrant ranges from 180 to 270 degrees.
4. The fourth quadrant ranges from 270 to 360 degrees.
Since θ = 150 degrees falls within the range of 90 to 180 degrees, it would be located in the second quadrant.
Now, let's move on to transforming the polar equation r = 10 cos θ into Cartesian coordinates. To do this, we need to substitute the polar coordinates (r, θ) with their corresponding Cartesian coordinates (x, y).
The conversion formulas are as follows:
- x = r cos θ
- y = r sin θ
Given the equation r = 10 cos θ, we can substitute the values into the conversion formulas:
- x = 10 cos θ cos θ
- y = 10 cos θ sin θ
Simplifying further:
- x = 10 cos^2 θ
- y = 10 sin θ cos θ
So, we have transformed the polar equation r = 10 cos θ into Cartesian coordinates as:
- x = 10 cos^2 θ
- y = 10 sin θ cos θ