# 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).

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- IndikosLv 74 years agoFavourite 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

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