Eliminate - if x-acos- y-asin-

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Basic Trigonometric Identities

Eliminate θ...

Question

Eliminate $θ$ , if $x = a cos θ, y = a sin θ$ .

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Solution

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θ

x = a cos θ + b sin θ

y = a sin θ - b cos θ

\frac{d y}{d x}

x = a (cos θ + θ sin θ)

y = a (sin θ - θ cos θ)

x = a (cos θ + θ sin θ), y = a (sin θ - θ cos θ),

\frac{d^{2} x}{d θ^{2}} = a (cos θ - θ sin θ), \frac{d^{2} y}{d θ^{2}} = a (sin θ + θ cos θ)

x = a cos θ, y = a sin θ

\frac{d^{2} y}{d x^{2}}

θ \neq K π, K \in Z

\frac{d^{2} x}{d θ^{2}} = a (\cos θ - θ \sin θ), \frac{d^{2} y}{d θ^{2}} = a (\sin θ + θ \cos θ) and \frac{d^{2} y}{d x^{2}} = \frac{\sec^{3} θ}{a θ} .

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