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which statement describes the graph and orientation of the parametric equations x = 16 cos r and y = 16 sin t?
A. The graph is a circle with a radius of 4. The orientation is counterclockwise as t increases.
B. The graph is a circle with a radius of 16. The orientation is counterclockwise as t increases.
C. The graph is the circle with the radius of 4. The orientation is clockwise as t increases.
D. the graph is a circle with a radius of 16. the orientation is clockwise as t increases.

Which is the polar form of the parametric equations x = 3t and y = t^2
A. r = 9 sec theta
B. r = 9 tan theta sec theta
C. r = 9tan^2 theta
D. r = 9sec^2 theta

Sagot :

Lanuel

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:

  • t is the angle.
  • 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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