(1 pt) find a parametrization of the ellipse centered at the origin in the xy-plane that has major diameter 14 along the x-axis, minor diameter 10 along the y-axis, and is oriented counter-clockwise. your parametrization should make the point (7,0) correspond to t=0. use t as the parameter for all of your answers.

Step-by-step explanation:

The parametrization of an ellipse center at origin and counter-clockwise is given by the formulas:

Where “a” is the radius of the major axis along the x-axis and “b” is the radius of the minor axis along the y-axis. Since the major diameter along the x-axis is 14 then its radius is its half, thus a=7. Similarly, since the minor diameter along the y-axis is 10, then its radius is half of it, thus b=5

Therefore, the parametric equations for the ellipse become:

Notice at t=0 we get:

which satisfies that the parametrization at t=0 makes the point (7,0)

sec ф = 5/3 (quadrant 4)

let x = base

y = perp

z = hypotenuse

sec ф = hypotenuse/base = 5/3

⇒ z = 5 and x = 3

finding y:

z² = x² + y²

5² = 3² + y²

y² = 25-9

y² = 16

y = 4

now finding all other geometric functions of theta:

sin ф = y/z = 4/5

sin ф = -4/5 (sin is negative in the 4th quadrant)

cos ф = x/z = 3/5

cos ф = 3/5 (cos is positive in 4th quadrant)

tan ф = y/x = 4/3

tan ф = -4/3 (tan is negative in 4th quadrant)

cosec ф = z/y = 5/4

cosec ф = -5/4 (cosec is negative in the 4th quadrant)

cot ф = x/y = 3/4

tan ф = -3/4 (tan is negative in 4th quadrant)

hello from mrbilldoesmath!

answer:

the domain is the set { -2, 0, 2, 3}

discussion:

the domain is the set of x values in the ordered pairs (x,y). taking the x, or first component, of each ordered pair gives   -2, 0, 2, 3.

you,

mrb