Parametrics and Polar Equations

Front

What is the rectangular form of the parametric equations x = 2t and y = t² + 3?

Back

y = ¼ x² + 3

Front

How do you calculate the horizontal distance traveled by a projectile?

Back

Horizontal distance = initial speed * cos(angle) * time

Front

Convert the polar coordinates (6, 2π/3) to rectangular form.

Back

(-3, 3√3)

Front

What is the polar form of the Cartesian equation x² + y² = 9?

Back

r = 3

Front

How do you find the angle in polar coordinates from rectangular coordinates?

Back

θ = arctan(y/x)

Front

What is the relationship between parametric equations and their rectangular form?

Back

Parametric equations can be eliminated to find a single rectangular equation.

Front

What is the formula for converting polar coordinates (r, θ) to rectangular coordinates (x, y)?

Back

x = r * cos(θ), y = r * sin(θ)

Front

How do you convert the equation y = 2x + 1 to polar form?

Back

r sin(θ) = 2r cos(θ) + 1

Front

What does the point (3, 3π/4) represent in polar coordinates?

Back

It represents a point in the second quadrant.

Front

What is the significance of the angle in polar coordinates?

Back

It determines the direction of the point from the origin.