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bixtya [17]
2 years ago
11

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

Mathematics
1 answer:
Margaret [11]2 years ago
6 0

Answer:

  x = 3π/2

Step-by-step explanation:

The given equation can be rewritten as a quadratic in sin(x), then solved by factoring.

<h3>Rewrite</h3>

Using the identity ...

  cos²x = 1 -sin²x

the equation can be rewritten as ...

  sin(x) = -(1 -sin²(x)) -1 . . . . . .substitute for cos²x

<h3>Solution</h3>

The new equation can be solved by considering it a quadratic in sin(x).

  0 = sin²(x) -sin(x) -2 . . . . . . subtract sin(x)

  (sin(x) -2)(sin(x) +1) = 0 . . . . factor quadratic

The solutions to this are ...

  sin(x) -2 = 0   ⇒   sin(x) = 2 . . . .  no solutions

  sin(x) +1 = 0   ⇒   sin(x) = -1   ⇒   x = 3π/2 (one solution)

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Answer:

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Step-by-step explanation:

The best way to rewrite this equation is to use the distributive property.

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Or, we can just use the commutative property to switch the numbers around, but I recommend the distributive.

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Hope this helps!

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horrorfan [7]
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The correct answer is 6.25 times.

This is how you get there:

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If you did this problem the other way, you would've ended up with .16. If you put the sizes into perspective, you will notice that this is highly unlikely.

I hope that I have been able to simplify this problem for you!

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Answer:

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Step-by-step explanation:

hope it helps :D

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