If cos(x) = 3/5 and sin x < 0, find sin(2x) as a fraction in simplest terms. sin(2x) =

Mathematics High School

If cos(x) = 3/5 and sin x < 0, find sin(2x) as a fraction in simplest terms.
sin(2x) =

Answers

Answer 1

Answer:

NOT 24/25 and NOT -4/5

Step-by-step explanation:

took the quiz

Answer 2

If cos(x) = 3/5 and sin x < 0, sin(2x) is equal to -24/25 as a fraction in simplest terms.

To find sin(2x), we can use the double-angle formula for sine:

sin(2x) = 2 * sin(x) * cos(x)

Given:

cos(x) = 3/5

sin(x) < 0

We need to determine sin(x) based on the given information.

Using the Pythagorean identity, sin^2(x) + cos^2(x) = 1:

[tex](sin(x))^2 + (cos(x))^2 = 1\\(sin(x))^2 + (3/5)^2 = 1\\(sin(x))^2 + 9/25 = 1\\(sin(x))^2 = 1 - 9/25\\(sin(x))^2 = 16/25[/tex]

sin(x) = -4/5

Now we can the values into the double-angle formula for sine:

sin(2x) = 2 * sin(x) * cos(x)

sin(2x) = 2 * (-4/5) * (3/5)

sin(2x) = (-8/5) * (3/5)

sin(2x) = -24/25

Therefore, sin(2x) is equal to -24/25 as a fraction in simplest terms.

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Step-by-step explanation:

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Answers

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Answers

Answer:

Step-by-step explanation:

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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

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Answers

Answer:

Step-by-step explanation:

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Answer:

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Answers

Answer:

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Step-by-step explanation:

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Answers

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Step-by-step explanation:

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Answers

Answer:

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Step-by-step explanation:

GOT IT RIGHT ON EDGE

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Step-by-step explanation:

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