Mathematics College

What is the exact value of Tan(pi/12)

Answers

Answer 1

We have

0 < π/12 < π/2

and

tan(π/12) = sin(π/12) / cos(π/12)

Both sin(x) and cos(x) are positive for 0 < x < π/2, so we expect tan(π/12) to also be positive.

Recall the double-angle identities for cosine,

cos²(x) = (1 + cos(2x)) / 2

as well as the Pythagorean identity,

tan²(x) = sec²(x) - 1

and by definition,

sec(x) = 1 / cos(x)

Putting everything together, we have

tan(x) = √(1 / cos²(x) - 1)

tan(x) = √(2 / (1 + cos(2x)) - 1)

Let x = π/12. Then 2x = π/6, and cos(π/6) = √3 / 2, so that

tan(π/12) = √(2 / (1 + cos(π/6)) - 1)

tan(π/12) = √(2 / (1 + √3 / 2) - 1)

tan(π/12) = √(4 / (2 + √3) - 1)

tan(π/12) = √(4 / (2 + √3) - (2 + √3) / (2 + √3))

tan(π/12) = √((2 - √3) / (2 + √3))

tan(π/12) = √(7 - 4 √3)

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Answer:

Step-by-step explanation:

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Answers

Answer:

4450 I think

Step-by-step explanation:

4878-428=4450

The difference in altitude and desert valley is 53.06 feet.

What is Integer?

Integers come in three types:

Zero (0)Positive Integers (Natural numbers)Negative Integers (Additive inverse of Natural Numbers)

Given:

The desert valley that is 428 feet below sea level is (-428).

and, altitude of 4878 feet is (+4878) feet.

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Step-by-step explanation:

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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

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Step-by-step explanation:

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I hope this helps in any way.

The mixed form of the factor 32/5 will be 6²/₅.

To convert the fraction 32/5 to a mixed number, we need to find the whole number part and the fractional part.

Divide the numerator (32) by the denominator (5) to find the whole number part. In this case, 32 divided by 5 equals 6 with a remainder of 2.

The quotient, 6, represents the whole number part of the mixed number.

The remainder, 2, represents the numerator of the fractional part.

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Putting it all together, the mixed number representation of 32/5 is 6 and 2/5.

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