Convert to Rectangular: r*tanΘ/secΘ=2
tanθ/secθ = sinθ
so, can you convert
r sinθ = 2
??
Can you answer the question and not be rude
To convert the given expression from polar coordinates to rectangular coordinates, we need to rewrite the trigonometric functions in terms of basic rectangular functions (sine, cosine, tangent).
Given expression: r * tan(Θ) / sec(Θ) = 2
First, let's substitute the expressions for tangent and secant in terms of sine and cosine:
r * (sin(Θ) / cos(Θ)) / (1 / cos(Θ)) = 2
Now, simplify the expression by multiplying the numerator and denominator on the left side by cos(Θ):
r * (sin(Θ) * cos(Θ) / cos(Θ)^2) = 2
Cancel out cos(Θ) in the numerator and denominator:
r * sin(Θ) = 2 * cos(Θ)^2
Next, we need to express sin(Θ) and cos(Θ) in terms of x and y (rectangular coordinates):
In a right triangle, sin(Θ) = y / r and cos(Θ) = x / r, where x and y represent the coordinates in the rectangular system.
Substituting these values into the equation:
r * (y / r) = 2 * (x / r)^2
Simplify further by canceling out the 'r' terms:
y = 2 * (x / r)^2
Since r represents the distance from the origin to the point in question, we can replace (x / r)^2 with r^2 using the Pythagorean theorem:
y = 2 * r^2
Hence, the rectangular form of the given expression is y = 2 * r^2.