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zheka24 [161]
2 years ago
10

What is the solution to the trigonometric inequality 2sin(x)+3>sin^2(x) over the interval 0<=x<=2pi radians?

Mathematics
1 answer:
devlian [24]2 years ago
7 0

2 sin(x) + 3 > sin²(x)

can be rewritten as

sin²(x) - 2 sin(x) - 3 < 0

(sin(x) - 3) (sin(x) + 1) < 0

The left side is equal to zero when either

sin(x) - 3 = 0   or   sin(x) + 1 = 0

sin(x) = 3   or   sin(x) = -1

The first case can never happen for real x, since |sin(x)| ≤ 1. From the second case, we get one zero in the interval 0 ≤ x ≤ 2π at x = 3π/2.

Now, split up the solution domain into two intervals, and check the sign of the left side of the inequality at some point in the interval. If the inequality holds up, that interval will belong to the solution set for the inequality.

• From 0 ≤ x < 3π/2, take x = 0. Then

sin²(0) - 2 sin(0) - 3 = 0² - 0 - 3 < 0

is true.

• From 3π/2 < x ≤ 2π, take x = 2π. Then

sin²(2π) - 2 sin(2π) - 3 = 0² - 0 - 3 = -3 < 0

is also true.

This means both intervals 0 ≤ x < 3π/2 and 3π/2 < x ≤ 2π satisfy the inequality.

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Answer:

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Step-by-step explanation:

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As previously said, the percent is always over 100. (x/100)

In this problem you are given the part (14) and the whole (25). So it would be 14/25. The percent in this problem would be x/100. Now to find percent with the given part/whole, you would multiply 14 with 100. Then simply divide by 25.

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see the explanation

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