Question

If tan 3 theta = 1, 0 < theta < Pi , then which of the following is true:
a) theta = arctan 1/3
b) theta = pi/12
c) theta = 1/3 arc tan pi/4
d) sec 3 theta = 2

Answer 1

your idea?

Answer 2

not sure

Answer 3

try once, please.

Answer 4

\(tan(3\theta) =1\)
\(3\theta =??\)

Answer 5

1/tan

Answer 6

not that, it is \(3\theta = arctan 1\) are you familiar with it?

Answer 7

not yet

Answer 8

we can go back and forth between an angle and its trigs, For example
\[sin\dfrac{\pi}{4}=\dfrac{\sqrt{2}}{2}\\\rightarrow \dfrac{\pi}{4}=arcsin(\dfrac{\sqrt{2}}{2})\]
your case is tan
\[tan(3\theta)=1\\\rightarrow 3\theta = arctan(1)\]

Answer 9

you can go another way like this, tan (??) = 1
and we know, tan (pi/4) =1