find all solutions for

tan^2 theta -4 = 0

i got theta = arctan 2

is that correct? and if it is how would i write it as a solution?

1 answer

theta = arctan2 or arctan -2
because tan^2 = 4, so tan is +/- 2

that's as exact as you can get. Just as pi or sqrt(7) is a perfectly valid number, so is arctan(2)

just be sure to note that since arctan(-2) = pi-arctan(2), the complete solution set is

k*pi+/-Arctan(2)

where Arctan(2) is the principal value.