Help Notes: `m = -1` find the inclination 'theta' (in radians and degrees) of the line with slope m.

Monday, 16 October 2017

$\displaystyle{m}=-{1}$ find the inclination 'theta' (in radians and degrees) of the line with slope m.

The given slope is $\displaystyle{m}=-{1}$ .

Take note that if the slope of the line is given, to determine the angle of inclination, apply the formula:

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

where $\displaystyle\theta$ is the angle measured counterclockwise from the positive x-axis going to the right of the line. And its range of values is from 0 to 180 degree only $\displaystyle{\left({{0}}^{{o}}\leq\theta\leq{{180}}^{{o}}\right)}$ .

Plugging in the value of m, the...

The given slope is $\displaystyle{m}=-{1}$ .

Take note that if the slope of the line is given, to determine the angle of inclination, apply the formula:

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

Plugging in the value of m, the formula becomes:

$\displaystyle{\tan{\theta}}=-{1}$

Then, take the inverse of tangent to isolate theta.

$\displaystyle\theta={{\tan}}^{{-{1}}}$

$\displaystyle\theta=-\frac{\pi}{{4}}{r}{a}{d}=-{{45}}^{{o}}$

Take note that when the computed value is negative, to get value of angle of inclination in the interval $\displaystyle{{0}}^{{o}}\leq\theta\leq{{180}}^{{o}}$ , add 180 degree (pi rad).

$\displaystyle\theta=-\frac{\pi}{{4}}+\pi=\frac{{{3}\pi}}{{4}}$ rad

$\displaystyle\theta=-{{45}}^{{o}}+{{180}}^{{o}}={{135}}^{{o}}$

Therefore, in radians, the angle of inclination is $\displaystyle\frac{{{3}\pi}}{{4}}$ rad. And in degree, the angle of inclination is $\displaystyle{{135}}^{{o}}$ .

Help Notes

Monday, 16 October 2017

$\displaystyle{m}=-{1}$ find the inclination 'theta' (in radians and degrees) of the line with slope m.

No comments:

Post a Comment

How can a 0.5 molal solution be less concentrated than a 0.5 molar solution?