Question

find two angles between 0° and 360° for the given condition. express your answer in terms of degrees. tanθ = √3. the angles are and .

Explanation:

Step1: Recall tangent - angle relationship

We know that $\tan\theta=\sqrt{3}$. The principal - value of $\theta$ for which $\tan\theta=\sqrt{3}$ is $\theta = 60^{\circ}$ since $\tan60^{\circ}=\sqrt{3}$ and the tangent function $y = \tan\theta$ has a period of $180^{\circ}$.

Step2: Find all solutions in the given range

The general solution of the equation $\tan\theta=\tan\alpha$ is $\theta=n\times180^{\circ}+\alpha$, where $n\in Z$. For $\alpha = 60^{\circ}$, when $n = 0$, $\theta=60^{\circ}$; when $n = 1$, $\theta=180^{\circ}+60^{\circ}=240^{\circ}$. Since we want solutions between $0^{\circ}$ and $360^{\circ}$, the two angles are $60^{\circ}$ and $240^{\circ}$.

Answer:

$60^{\circ}$, $240^{\circ}$