MATHEMATICS HIGH SCHOOL

The exact value of tan 5pi/12 is?

Answers

Answer 1

Answer:

Answer:

The exact value of $\tan ((5\pi)/(12))$ is $2+√(3)$

Step-by-step explanation:

We need to calculate the exact value of $\tan ((5\pi)/(12))$

Since, $\tan (x)/(2) = (1- \cos x)/(\sin x)$

Put $x= (5 \pi)/(6)$ in above

$\tan ((5\pi)/(12)) = (1- \cos (5\pi)/(6))/(\sin (5\pi)/(6))$

Since,

$\cos (5\pi)/(6)}=(-√(3))/(2)$

$\sin (5\pi)/(6)}=(1)/(2)$

$\tan ((5 \pi )/(12)) = (1+(√(3))/(2))/((1)/(2))$

$\tan ((5 \pi )/(12)) = ((2+√(3))/(2))/((1)/(2))$

$\tan ((5 \pi )/(12)) = 2+√(3)$

Therefore, the exact value of $\tan ((5\pi)/(12))$ is $2+√(3)$

Answer 2

Answer:

The exact value of tan(5π/12) is √(2/3).

How to determine the exact value of tan 5pi/12

The exact value of tan(5π/12) can be calculated using trigonometric identities and reference angles.

The angle 5π/12 is not a special angle with a known tangent value, so we need to work with its reference angle, which is π/12.

Using the identity tan(θ) = sin(θ) / cos(θ), we can express tan(π/12) as:

tan(π/12) = sin(π/12) / cos(π/12)

Now, let's find the exact values of sin(π/12) and cos(π/12) using half-angle and double-angle formulas:

sin(π/12) = sin(π/6) / 2^(1/2)

= 1 / 2^(1/2) / 2

= (2^(1/2)) / 4

= √2 / 4

cos(π/12) = cos(π/6) / 2^(1/2)

= 3^(1/2) / 2 / 2^(1/2)

= 3^(1/2) / 4√2

= (√3) / 4

Now, we can substitute these values back into the expression for tan(π/12):

tan(π/12) = sin(π/12) / cos(π/12)

= (√2 / 4) / (√3 / 4)

= (√2 / 4) * (4 / √3)

= √2 / √3

= √(2/3)

Therefore, the exact value of tan(5π/12) is √(2/3).

Learn more about trigonometric identities at brainly.com/question/25618616

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Step-by-step explanation:

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Answers

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Answer:

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Step-by-step explanation:

Tony had 1 1/2 gallons of orange juice. He drank 2/7 of the orange juice he had. How mucj orange juice did Tony drink?

Answers

Answer:

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Step-by-step explanation:

Amount of orange juice Tony had is $1(1)/(2)$ gallons.

Amount of orange juice drank by him is $(2)/(7)$ of the orange juice he had.

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