Parametric Equation for a Curve with Cosine and Sine Functions

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To find the equation y=f(x) for the parametric curve defined by x = cos(theta) and y = cos(theta) + sin^2(theta), it is essential to express y in terms of x. The relationship between sine and cosine can be utilized, specifically using the identity sin^2(theta) = 1 - cos^2(theta). By substituting cos(theta) with x, the equation for y can be rewritten as y = x + (1 - x^2). This simplifies to y = 1 - x^2 + x, providing the desired function in terms of x. The solution effectively demonstrates the application of trigonometric identities in converting parametric equations to Cartesian form.
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Homework Statement



Find an equation y=f(x) for the parametric curve x = cos (theta) y = cos (theta) + sin^(2) (theta)

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The Attempt at a Solution


I know I need to solve for theta but I'm not sure how to go about this. Can I plug x into the theta's in y or do I use the trig identity sin^(2) + cos^(2) = 1? Thanks in advance!
 
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Use the fact that \cos\theta=x and \sin^2\theta=1-\cos^2\theta.
 

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