Maths alevel - parametric Watch

studybloomer
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#1
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Hi,
I am stuck on working on the domain. I have already worked out the cartesian equation.
x= sec^2t+1 y=2sint -pi/4<t<pi/4
cartesian equation: y=square root of (8-4x/1-x)

How would I work out the domain and range?
The answer for the domain is x <1 or x>2

Thank you,
P.Abira
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mqb2766
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Domain: sub t into the expression for x and see what range it gives,then check that to make sure you can calculate the sqrt() expression in the cartesian equation.
Range: sub the values from the domain into the cartesian equation

May help:
https://www.desmos.com/calculator/oximuosldk

(Original post by studybloomer)
Hi,
I am stuck on working on the domain. I have already worked out the cartesian equation.
x= sec^2t+1 y=2sint -pi/4<t<pi/4
cartesian equation: y=square root of (8-4x/1-x)

How would I work out the domain and range?
The answer for the domain is x <1 or x>2

Thank you,
P.Abira
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reply
studybloomer
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#3
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I did sub in the value of t :-pi/4 in to the x expression, but instead i got x=3 for both positive and negative t values (pi/4).

However, the answer says x <1 or x>2.

Also what do you mean by this: '' then check that to make sure you can calculate the sqrt() expression in the cartesian equation.''

Thanks
(Original post by mqb2766)
Domain: sub t into the expression for x and see what range it gives,then check that to make sure you can calculate the sqrt() expression in the cartesian equation.
Range: sub the values from the domain into the cartesian equation

May help:
https://www.desmos.com/calculator/oximuosldk
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mqb2766
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Those values of x make the sqrt() argument positive as indeed it should be. If its the domain and range of the cartesian function, then that's the answer. I'm not sure why they don't take it back to the original parametric equation as this imposes extra constraints on x.

Edit: To get a range of values, you can't always just sub the end points in.
(Original post by studybloomer)
I did sub in the value of t :-pi/4 in to the x expression, but instead i got x=3 for both positive and negative t values (pi/4).

However, the answer says x <1 or x>2.

Also what do you mean by this: '' then check that to make sure you can calculate the sqrt() expression in the cartesian equation.''

Thanks
Last edited by mqb2766; 1 month ago
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