How do you use a calculator to evaluate tan((5pi)/6)?

Feb 20, 2017
• 0.577

Explanation:

$\tan \frac{5 \pi}{6} = \tan \left(\frac{900}{6}\right) = \tan {150}^{\circ}$
Calculator --> tan 150 = - 0.577

Feb 21, 2017

$\tan \left(\frac{5 \pi}{6}\right) = - 0.57735027$

Explanation:

$\tan \left(\frac{5 \pi}{6}\right)$

$\therefore = \tan \left(\frac{5 \times 3.141592654}{6}\right)$

$\therefore = \tan \left(\frac{15.70796327}{6}\right)$

$\therefore = \tan 2.617993878$

$\therefore = - 0.57735027$

Note

• (1) you can choose value of $\pi$ from calculator and then multiply it by $5$ and then divide by $6$ to get $2.617993878$

• (2) the angle $2.617993878$ is in radians, hence choose the mode for angles in radians

• (3) and then in calculator choose ratio tan to get $\tan \left(\frac{5 \pi}{6}\right)$

You can also use ${180}^{\circ}$, in place of $\pi$, to start entering angle directly in degrees and then multiplying by $5$ and dividing by $6$ gives $150$ in degrees and $\tan {150}^{\circ} = - 0.57735027$

Feb 21, 2017

$\therefore = - 0.577350269$

Explanation:

To convert radians to degrees multiply by $\frac{180}{\pi}$

To convert degrees to radians multiply by $\frac{\pi}{180}$

$\tan \left(\frac{5 \pi}{6}\right)$ radians

$\therefore = \tan \left(\left(\frac{5 {\cancel{\pi}}^{1}}{\cancel{6}} ^ 1\right) \times {\cancel{180}}^{30} / {\cancel{\pi}}^{1}\right)$ degrees

:.=tan(150°)

$\therefore = - 0.577350269$