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Explain the solution to tan3x=1.

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susank7780 | Student, Grade 11 | Salutatorian

Posted May 21, 2013 at 1:55 AM via web

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Explain the solution to tan3x=1.

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ishpiro | Teacher | (Level 1) Associate Educator

Posted May 21, 2013 at 2:03 AM (Answer #1)

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tan (3x) = 1

The tangent of an angle is 1 when the angle is 45 degrees (`pi/4` in radians.)

Since the tangent function is periodic with the period of 180 degrees, or `pi` , tangent is 1 for any angle in radians expressed as

`pi/4 + pi*k` , where k is an integer (`k = 0, +-1, +-2...` )

So, tan (3x) = 1 when

`3x = pi/4 + pi*k`

Dividing both sides by 3, obtain

`x = pi/12 +pi/3 *k`

So, the solution to the given equation is

`x = pi/12 + pi/3 * k` , where k is an integer

 

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