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m2003
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How does one prove that the curve r=sin(n{theta}) has n loops when n is odd and 2n loops when n is even?
The equation for this is r=sin(n{theta}), where r represents the distance from the origin and n represents the number of loops.
The number of loops can be determined by looking at the value of n in the equation. Each value of n corresponds to a specific number of loops, with n=1 representing one loop, n=2 representing two loops, and so on.
The variable theta represents the angle in radians. In this equation, it determines the shape and size of the loop.
No, the number of loops in this equation must be a positive integer. A negative number of loops would not make mathematical sense in this context.
Yes, the value of n can be a non-integer, such as a decimal or fraction. This would result in a more complex shape with a partial loop.