A designer models a point on a circular running track of radius 5 m as x = 5 \θ and y = 5 \θ , with \θ measured at the centre. Eliminating \θ , which equation do x and y always satisfy?

Question

Accepted Answer

x^2 + y^2 = 25. Squaring and adding: x^2 + y^2 = 25 ^2\θ + 25 ^2\θ = 25( ^2\θ + ^2\θ) = 25 . The Pythagorean identity does the whole job. Answering x^2 + y^2 = 5 forgets to square the radius as well; answering x + y = 5 adds the two equations instead of squaring them first.

A designer models a point on a circular running track of radius 5 m as $x = 5 cos θ$ and $y = 5 sin θ$ , with $θ$ measured at the centre.
Eliminating $θ$ , which equation do $x$ and $y$ always satisfy?

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More Class 10 Trigonometric Identities practice

A designer models a point on a circular running track of radius 5 m as x=5cosθ and y=5sinθ, with θ measured at the centre.Eliminating θ, which equation do x and y always satisfy?

Step-by-Step Solution

Master this chapter in 30 minutes a day.

More Class 10 Trigonometric Identities practice

A designer models a point on a circular running track of radius 5 m as $x = 5 cos θ$ and $y = 5 sin θ$ , with $θ$ measured at the centre.
Eliminating $θ$ , which equation do $x$ and $y$ always satisfy?