What times is the bird flying horizontally/vertically?

[dannyxyeah]

The flight of a bird follows the curve x=t-cos(t), y=3-2sin(t)... where 0<=t<=4pi is the time in seconds.
a) What times is the bird flying horizontally? find the (x,y) coordinates of the corresponding points.
b) What times is the bird flying vertically? find the (x,y) coordinates of the corresponding points.

my work:
i found dx/dt=1+sin(t)
dy/dt=-2cos(t)
and therefore dy/dx=(-2cos(t))/(1+sin(t))

The bird flies horizontally when dy/dt=0 and dx/dt=/=0, right?
dy/dt=0 at t=pi/2 and 3pi/2. However, dx/dt=0 when 3pi/2, so would it be just pi/2?

Same problem for part b. The bird flies vertically when dx/dt=0 and dy/dt=/=0.
dx/dt=0 at t=3pi/2, but dy/dt equals zero then. What does this mean for the bird's flight?

 

[SammyS]

The flight of a bird follows the curve x=t-cos(t), y=3-2sin(t)... where 0<=t<=4pi is the time in seconds.
a) What times is the bird flying horizontally? find the (x,y) coordinates of the corresponding points.
b) What times is the bird flying vertically? find the (x,y) coordinates of the corresponding points.

my work:
i found dx/dt=1+sin(t)
dy/dt=-2cos(t)
and therefore dy/dx=(-2cos(t))/(1+sin(t))

The bird flies horizontally when dy/dt=0 and dx/dt=/=0, right?
dy/dt=0 at t=pi/2 and 3pi/2. However, dx/dt=0 when 3pi/2, so would it be just pi/2?

Same problem for part b. The bird flies vertically when dx/dt=0 and dy/dt=/=0.
dx/dt=0 at t=3pi/2, but dy/dt equals zero then. What does this mean for the bird's flight?

Indeed, what does it mean if both dx/dt = 0 and dy/dt = 0 simultaneously ?

Also, don't forget, the flight is from t = 0 to t = 4π.

 

[dannyxyeah]

Indeed, what does it mean if both dx/dt = 0 and dy/dt = 0 simultaneously ?

Would it mean that the bird was either stationary or floating in place?

Also, don't forget, the flight is from t = 0 to t = 4π.

Ah, that means I need to include every interval of pi/2 up until 8pi/2 correct?

 

[SammyS]

Would it mean that the bird was either stationary or floating in place?

Stationary --- momentarily, but stationary.

Ah, that means I need to include every interval of pi/2 up until 8pi/2 correct?

Yes.

 

[dannyxyeah]

Stationary --- momentarily, but stationary.

Great, thank you!

Also, how do you interpret the "find the (x,y) coordinates of the corresponding points"? What do you reckon it's asking for? Just to plug in the different t values into each x and y equation initially given?

 

[SammyS]

Great, thank you! So I would omit any values of t at which dy and dx=0. Otherwise is my work correct? :D Also, how do you interpret the "find the (x,y) coordinates of the corresponding points"? What do you reckon it's asking for? Just to plug in the different t values into each x and y equation initially given?

Certainly, if dx/dt=0 and dy/dt=0, the bird is stationary, and thus is not flying in any direction.

To find the location at any particular time, yes, just plug the time into the expressions for x & y .

 

[dannyxyeah]

ignore this please. I got it :)