Home / 3\theta = 330^\circ + 360^\circ k \quad \Rightarrow \quad \theta = 110^\circ + 120^\circ k

3\theta = 330^\circ + 360^\circ k \quad \Rightarrow \quad \theta = 110^\circ + 120^\circ k

February 22, 2026

$3\theta = 330^\circ + 360^\circ k \quad \Rightarrow \quad \theta = 110^\circ + 120^\circ k$

\phi = 30^\circ + 360^\circ k \quad \text{or} \quad \phi = 330^\circ + 360^\circ k, \quad k \in \mathbb{Z}
Since $ \phi = 3\theta $, we substitute:
3\theta = 30^\circ + 360^\circ k \quad \Rightarrow \quad \theta = 10^\circ + 120^\circ k
We now find all $ \theta \in [0^\circ, 360^\circ] $ by plugging integer values of $ k $.
For $ \theta = 10^\circ + 120^\circ k $:
$ k = 0 $: $ 10^\circ $