Find a parametrization of the ellipse centered at the origin in the xy-plane that has major diameter 12 along the x-axis, minor diameter 8 along the y-axis, and is oriented counter-clockwise. Use t as the parameter. It should change from 0 to 2*pi. Your parametrization should make the point (6,0) correspond to t = 0.
x(t) =
y(t) =
(0 <= t <= 2*pi).

x = 6 cos t

y = 6 sin t

where t varies from 0 to 2pi

Step-by-step explanation:

Given that an ellipse is centred at the origin in xy plane.

So equation would be of the form

Major axis =2a= 12

so a=6

Minor diameter = 8

b = 8/2 = 4

a=6 and b =4

Also (6,0) should correspond to t=0

So best parametrization would be

x = 6 cos t

y = 6 sin t

where t varies from 0 to 2pi

-13

step-by-step explanation:

f(x)=2x-5 for f(-4)

f(-4)   means let x=-4

f(-4) = 2(-4) -5

f(-4) =-8-5

      = -13

(sin 42)/31. = sinx)/37

sinx = 37 (sin42)/31

= 37× 0.66/31 = 0.787

x= 51.9

other angle opposite to y = 180-51.9-42

= 180- 93.9 =86.1

so

sin42)/31 = sin 86.1)/y

0.021 = 0.997 /y

y= 0.997/0.021 =47.47