Write the equation in rectangular coordinates: #r=10sin(θ)#?
2 Answers
Explanation:
Given:
This is the graph in polar coordinates:
Multiply both sides by
Substitute
Add
Matching the right side of the pattern
We observe that the following equation will allow us to determine the value of k:
Substitute the left side of the pattern into equation [1] with
This is the Cartesian equation of a circle with center
This is the graph in Cartesian coordinates:
Please observe that the graphs are identical, therefore, the conversion is correct.
Explanation:
#"to convert from "color(blue)"polar to rectangular"#
#•color(white)(x)r=sqrt(x^2+y^2)rArrr^2=x^2+y^2#
#•color(white)(x)y=rsinthetarArrsintheta=y/r#
#r=10sintheta#
#rArrr=(10y)/r#
#"multiply both sides by r"#
#rArrr^2=10y#
#rArrx^2+y^2-10y=0#
#"completing the square on "y^2-10y" gives"#
#rArrx^2+(y-5)^2=25#
#"which is the equation of a circle"#
#"centre "=(0,5)" and radius "=5#
graph{x^2+(y-5)^2=25 [-20, 20, -10, 10]}