Question

Write the value of the tan inverse of $0.6666$ in degrees and minutes.

Answer 1

Determine the value of the ${\tan }^{-1}$of $0.6666$ in degrees and minutes.

Calculate the tan inverse value:

${\tan }^{-1}(0.6666)=0.58795645rad$

Convert the radian to a degree:

$$\begin{gathered} 0.58795645=0.58795645\times \frac{180}{\mathrm{\pi }}\mathrm{degrees}\left[\because \mathrm{\pi }=3.14159265359\right] \\ =0.58795645\times \frac{180}{3.14159265359}\mathrm{degrees} \\ =33.{687423024}^0 \end{gathered}$$

Since $1°=60\min .$

Hence,

$$\begin{gathered} {33.687423024}^0=33.687423024\times 60\text{'}\left[\because 1°=60\text{'}\right] \\ =2021.2453814\min \end{gathered}$$

Hence, the ${\tan }^{-1}$ of $0.6666$ is equivalent to ${33.687423024}^0$and also is equivalent to $2021.2453814\min .$