Convert the equation to polar form.
8x=8y
So far, I got this: 8*rcosθ = 8*rsinθ
But it's wrong.
8cosθ = 8sinθ is ok
then:
cosθ = sinθ
sinθ/cosθ = 1
tanθ = 1
θ = π/4
so our equation would simply be
θ = π/4
we have a similar situation for a vertical line in our x-y system
a vertical line would have the form x = k , no mention is made of the y, since the y
can be any value.
Similarly here, by saying θ = π/4 , we say that r can be any length as long
as our angle is 45°. That will give us the straight line y = x
To convert the equation 8x = 8y to polar form, you need to use the following conversions:
x = rcosθ
y = rsinθ
Let's rewrite the equation using these conversions:
8(rcosθ) = 8(rsinθ)
Now, let's simplify the equation:
8rcosθ = 8rsinθ
Divide both sides of the equation by 8:
rcosθ = rsinθ
However, it is important to note that this equation does not match the original equation of 8x = 8y. This indicates that there may have been an error in the initial conversion or equation setup. Please double-check your calculations and the original equation to identify any mistakes.
To convert the equation 8x = 8y to polar form, you need to express x and y in terms of r and θ.
Recall that in polar coordinates, x = rcosθ and y = rsinθ.
So, substituting these expressions into the equation, we have:
8(rcosθ) = 8(rsinθ)
Now, let's simplify the equation:
8rcosθ = 8rsinθ
To determine what went wrong in your attempt, it seems that you incorrectly multiplied both sides of the equation by r. In this case, you don't need to perform any multiplication on either side because the equation is already in terms of x and y.
To continue, let's simplify the equation further:
8cosθ = 8sinθ
Finally, we can divide both sides of the equation by 8 to get the final result in polar form:
cosθ = sinθ