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Find all solutions of the equation in the interval [0,2π].

a) 0
b) 2π
c) π
d) 3π/2


1 Answer

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Final answer:

To find solutions of an equation within the interval [0,2π], the specific function equated to zero is needed. For common trigonometric functions, certain angles within the interval naturally satisfy the condition of being equal to zero.

Step-by-step explanation:

To find all solutions of the equation in the interval [0,2π], we must first identify the equation in question. Since no specific equation is provided in the original inquiry, we'll presume that it is a simple trigonometric equation such x = 0, where x is the angle in radians. The solutions in the interval [0,2π] for x = 0 would be any angle where the given trigonometric function equals zero.

For a cosine function, for example, this would mean finding the angles where the cosine is zero which occurs at π/2 and 3π/2 within the given interval. Similarly, for a sine function, the angle where sine of x is zero would be at 0, π, and 2π. Without a specific function specified, the solutions provided in the options a) 0, b) 2π, c) π, d) 3π/2—can only be affirmed if they apply to the undisclosed trigonometric function in question.

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