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Eclair_de_XII
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Homework Statement
Eliminate the parameter and identify the graph of the pair of parametric equations. Determine the domain (the set of x-coordinates) and the range (the set of y-coordinates).
x = sin t, y = -3 sin t - 5
Homework Equations
y = -3x - 5
Domain: (-∞,∞)
Range: (-∞,∞)
The Attempt at a Solution
I've already solved this equation by substitution but I don't quite understand how the domain and the range are supposed to make sense. The domain of a sine function can't be higher than one or lower than negative one, right? Because sin2x + cos2x = 1, I don't believe that it's possible. Therefore, the domain of x cannot be (-∞,∞), and the domain of y cannot be (-∞,∞). Can someone explain to me how eliminating parameters is supposed to work?
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