Convert to Rectangular: r*tanΘ/secΘ=2
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y=2
y=½
x=2
x=½
tanθ/secθ = sinθ
Now do you have an idea?
To convert the given equation from polar form to rectangular form, we need to express the trigonometric functions in terms of x and y coordinates.
The equation is: r * tan(Θ) / sec(Θ) = 2
Let's start by transforming the tangent function. The tangent function is defined as: tan(Θ) = y / x
Substituting this into the equation, we have: r * (y / x) / sec(Θ) = 2
Next, we need to transform the secant function. The secant function is defined as: sec(Θ) = 1 / cos(Θ)
Substituting this into the equation, we have: r * (y / x) / (1 / cos(Θ)) = 2
To simplify further, we can convert r to its rectangular form using the conversion equations:
r = sqrt(x^2 + y^2)
Substituting this into the equation, we have: (sqrt(x^2 + y^2)) * (y / x) / (1 / cos(Θ)) = 2
Now, let's convert the remaining trigonometric functions:
cos(Θ) = x / r
Substituting this into the equation, we have: (sqrt(x^2 + y^2)) * (y / x) / (1 / (x / r)) = 2
Simplifying further by canceling out terms:
(sqrt(x^2 + y^2)) * (y / x) * (x / r) = 2
The x values cancel out, and we are left with:
(sqrt(x^2 + y^2)) * y / r = 2
Multiplying both sides by r to eliminate the denominator:
sqrt(x^2 + y^2) * y = 2r
Squaring both sides to eliminate the square root:
x^2 + y^2 * y^2 = 4r^2
Rearranging terms:
x^2 + y^4 = 4r^2
This is the equation in rectangular form.