Notes: `m = -7/9` find the inclination 'theta' (in radians and degrees) of the line with slope m.

Monday, April 21, 2014

$\displaystyle{m}=-\frac{{7}}{{9}}$ find the inclination 'theta' (in radians and degrees) of the line with slope m.

You need to use the following formula to evaluate the inclination angle theta, such that:

$\displaystyle{\tan{\theta}}={m}$

Replacing- $\displaystyle\frac{{7}}{{9}}$ for m, yields:

$\displaystyle{\tan{\theta}}=-\frac{{7}}{{9}}\Rightarrow\theta={{\tan}}^{{-{1}}}{\left(-\frac{{7}}{{9}}\right)}\Rightarrow\theta=-{{\tan}}^{{-{1}}}{\left(\frac{{7}}{{9}}\right)}$

$\displaystyle\theta=-{{37}}^{{o}}{50}'{49}''$

The answer in radians can be calculated such that:

$\displaystyle\theta=\frac{{-{{37}}^{{o}}{50}'{49}''\cdot\pi}}{{{{180}}^{{o}}}}$

$\displaystyle\theta=-{0.660}$ radians

Hence, evaluating the angle theta in degrees and radians yields $\displaystyle\theta=--{{37}}^{{o}}{50}'{49}''$ or $\displaystyle\theta$ = - 0.660 radians.

Notes

Monday, April 21, 2014

$\displaystyle{m}=-\frac{{7}}{{9}}$ find the inclination 'theta' (in radians and degrees) of the line with slope m.

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