Find all of the exact solutions to tan(7x)=1 within the interval [0,2pi)?

I know that x is equal to (x+4npi)/28. I am struggling with finding all of the solutions on the interval [0,2pi).

2 Answers

Relevance
  • 4 years ago
    Favourite answer

    tan(7x) = 1

    7x = arctan(1) = pi/4 + n*pi, n integer

    x = pi(4n+1)/(4*7)

    since we are interested for 0 <= x < 2pi

    or pi(4n+1)/28 < 2pi

    or 4n+1 < 56

    or 4n < 55

    or n < 13 3/4

    so n = 0,1,2,3,......, 13

    so roots are x = pi(4n+1)/28, n=0,1,2,........., 13

  • alex
    Lv 7
    4 years ago

    What is " x is equal to (x+4npi)/28 " ?

    tan(7x)=1 --->7x = (pi/4)+ n pi

    so x = ...

Still have questions? Get answers by asking now.