Posted by **help?** on Friday, October 28, 2011 at 10:12pm.

(3 tan^2x-1)(tan^2-3)= 0

can someone please explain how to do this problem and then explain the whole pie thing at the end...like, this is suppose to equal pie/6 b/c it's tan...im soooo confused.....

- trig -
**Reiny**, Friday, October 28, 2011 at 10:53pm
(3 tan^2x-1)(tan^2-3)= 0

so 3tan^2x = 1 or tan^2x = 3

tan^2x = 1/3 or tan^2x = -3

the second part has no solution, since something^2 cannot be negative

tanx = ± 1/√3

so x is in any of the 4 quadrants.

form the 30-60-90 triangle we know that

tan 30°

so in degrees, x = 30°, 150°, 210° and 330°

It appears that we are to give the answers in radians, and you seem to know very little about radians.

I am sure your texbook has a unit on it, or else you can learn about it on the thousands of webpages found after googling "radians"

in short, πradians = 180°

so π/6 = 30° , by dividing both sides of the equation above by 6

further:

150° = 5π/6

210° = 7π/6

330° = 11π/6

- trig -
**drwls**, Friday, October 28, 2011 at 10:57pm
Your equation is already factored. You have a solution if either factor is zero.

tan^2x can be either 1/3 or 3

tan x = +or- 1/sqrt3

tanx = +or- sqrt3

x = 30, 60, 120, 150, 210, 240, 300 or 330 degrees

pi/6 radians (30 degrees) is only one of the answers.

- my bad! - trig -
**Reiny**, Friday, October 28, 2011 at 11:39pm
Go with drwls solution.

somehow my +3 changed into a -3 for the second factor. there are 4 more solutions from that, as drwls shows.

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