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a level maths question on parametric equation

the question im stuck on is part b and this question from the pure textbook y2
the path on a ferris wheel at time t minutes is modelled using the parametric equations x=12sint , y=12-12cost
where x is the horizontal distance in metres of the car from the start of the ride and y is the height in metres above the ground.
a) show that the motion of the car is a circle with radius 12m.
b)hence, find the maximum height of the car during the journey.
the answer is worked out using t=pi
which i don't understand

any help is helpful
Reply 1
Avatar for mqb2766
mqb2766
21
Original post by bxcvxcvxv
the question im stuck on is part b and this question from the pure textbook y2
the path on a ferris wheel at time t minutes is modelled using the parametric equations x=12sint , y=12-12cost
where x is the horizontal distance in metres of the car from the start of the ride and y is the height in metres above the ground.
a) show that the motion of the car is a circle with radius 12m.
b)hence, find the maximum height of the car during the journey.
the answer is worked out using t=pi
which i don't understand

any help is helpful


If it's b) what value of t maximizes the height (y)?
Reply 2
Avatar for Em2111
Em2111
8
Is it the 't=pi' part you don't understand or how to actually do the question? If it's the former, it means that the question is in radians. This is just another way of expressing angles, with pi being the same as 180 degrees. To work out question a), sub the expressions you are given into the equation for a circle.
Original post by Em2111
Is it the 't=pi' part you don't understand or how to actually do the question? If it's the former, it means that the question is in radians. This is just another way of expressing angles, with pi being the same as 180 degrees. To work out question a), sub the expressions you are given into the equation for a circle.

yh i guess i don't understand how to actually do the question for part b
Reply 4
Avatar for mqb2766
mqb2766
21
Original post by bxcvxcvxv
yh i guess i don't understand how to actually do the question for part b

The height is y
12 - 12 cos(t)
What range of values can this (cos) take and what is the value of t that gives the largest value?
Original post by mqb2766
If it's b) what value of t maximizes the height (y)?

isnt it pi/2 from the sin graph
Reply 6
Avatar for mqb2766
mqb2766
21
Original post by bxcvxcvxv
isnt it pi/2 from the sin graph

The height is y, not x. So the cos curve is what you want.
Original post by mqb2766
The height is y, not x. So the cos curve is what you want.

ah makes sense so the cos has a maximum at 0 degrees and 360
Reply 8
Avatar for mqb2766
mqb2766
21
Original post by bxcvxcvxv
ah makes sense so the cos has a maximum at 0 degrees and 360

Yes, but use radians. You're interested in when -cos() has a maximum.
Original post by mqb2766
Yes, but use radians. You're interested in when -cos() has a maximum.

thank you so much i get why its PI
flip the cos graph and then the max is at pi

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