Question

Solving linear trig equations?

Solve tan(3x)=1 if -pi≤x≤pi.

answer: x=pi/12, 5pi/12, 3pi/4, -pi/4, -7pi/12, -11pi/12

I don't get how you do this question.. I know that the restrictions become -3pi≤3x≤3pi but i can't do beyond that.. can somebody please help?

Answer 1

Principle angle = arctan(1) = pi/4.

=> 3x = pi/4

Also, tan(a) = tan(b) <=> a = pi*n + b
=> 3x also equals pi/4 +/- pi within the restriction +/-3pi.

Then divide all these by 3.

Answer 2

I still don't get it... I can't until 3x = pi/4 :S

Answer 3

Oh dear :(. You need to go re-learn it then

Answer 4

I just don't get the restriction part of it.. if it's 0≤x≤2pi, I can do most questions but if it's -pi≤x≤pi or other "complicated" ones, I can't do it

Answer 5

It's exactly the same principle (especially for tan) ...