From the graph and orientation of the parametric equations: A. the graph is a circle with a radius of 4. The orientation is counterclockwise as t increases.
How to find a polar function?
In geometry, the relationship between the rectangular coordinates (x, y) and polar coordinates (r, t) is given by these polar functions:
x = rcost and y = rsint.
Where:
- r is the radius of a circle.
Mathematically, the standard form of the polar equation of a circle is given by;
x² + y² = r²
Given the following data;
x = 16cost ⇒ x² = 16cos²t
y = 16sint ⇒ y² = 16sin²t
Evaluating, we have:
x² + y² = 16
r² = 16
r = √16
Radius, r = 4.
Also, the orientation is counterclockwise as t increases because the angle gets bigger (increases).
How to determine polar form of the parametric equations?
x = 3t .....equation 1.
y = t² .....equation 2.
Making t the subject of formula in eqn. 1, we have:
t = x/3 .....equation 3.
Substituting eqn. 3 into eqn. 2, we have:
y = (x/3)²
rsinθ = (rcosθ/3)²
rsinθ = r²cos²θ/9
9rsinθ = r²cos²θ
9sinθ = rcos²θ
r = 9sinθ/cos²θ
r = 9 × (sinθ/cosθ) × 1/cosθ
r = 9tanθsecθ.
Read more on polar coordinates here: https://brainly.com/question/2193539
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