3 tan^2 7x = 1

Question

How many answers would you expect this equation to have on [0,2π)? Explain why.

Answer 1

3tan^2(7x) = 1

tan^2(7x) = 1/3

tan(7x) = + or - sqr(1/3)

7x = the angle whose tangent = + or - about .577

7x = 30 degrees or 210 degrees

x = about 30/7 = + or - 4.29 degrees or (180+30)/7 = 210/7 = 30 degrees or 150/7 = about 21.4 degrees

tan30 = 1/sqr3

tan^2(30) = 1/3

1/3 times 3 = 1

4 different answers, +4.3, -4.3, 30 and 21.4