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Prove that the equation sinx = 0.3 has at least one solution.

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Answer:

Explanation:

To prove that the equation sin(x) = 0.3 has at least one solution, we can use the Intermediate Value Theorem.

1. The Intermediate Value Theorem states that if a continuous function takes on two different values at two different points, then it must also take on every value between those two points.

2. The function sin(x) is a continuous function.

3. The value 0.3 is between -1 and 1, which are the range of values of the sine function.

4. Therefore, by the Intermediate Value Theorem, there must exist at least one value of x for which sin(x) = 0.3.

In other words, the equation sin(x) = 0.3 has at least one solution.

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User Sean Hogan
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