Transform the polar equation to a Cartesian (rectangular) equation: r= 4sinθ options include:

x^2+y^2 = 4y

x^2+y^2 = -4

x^2+y^2 = 4

x^2+y^2 = -4y

  x^2 +y^2 = 4y

Step-by-step explanation:

Using the usual translation relations, we have ...

  r^2 = x^2+y^2

  x = r·cos(θ)

  y = r·sin(θ)

Substituting for sin(θ) the equation becomes ...

  r = 4sin(θ)

  r = 4(y/r)

  r^2 = 4y

Then, substituting for r^2 we get ...

  x^2 +y^2 = 4y . . . . . matches the first choice

the correct answer is x/3+10≥32

hope this !

p ÷ r = tan(x)

step-by-step explanation:

given that there is a figure below shows a right triangle: a right triangle is shown with hypotenuse equal to q units and the length of the legs equal to p units and r units.

graph is missing so i will create the graph as per given information.

the angle between the legs having lengths p units and q units is y degrees. the angle between the legs having lengths r units and q units is x degrees.

now we need to find about what is p ÷ r equal to.

so we can use trigonometric ratio tan(x)=[altitude]/[base] to find the value of p ÷ r, because p is the altitude and r is the base.

p ÷ r=tan(x)

hence final answer is p ÷ r=tan(x).