Notes: `(sqrt(2), 2), (0, 1)` Find the inclination 'theta' (in radians and degrees) of the line with slope m.

Thursday, February 3, 2011

Given $\displaystyle{\left(\sqrt{{2}},{2}\right)},{\left({0},{1}\right)}$

Find the slope using the formula

$\displaystyle{m}=\frac{{{y}_{{2}}-{y}_{{1}}}}{{{x}_{{2}}-{x}_{{1}}}}$

$\displaystyle{m}=\frac{{{1}-{2}}}{{{0}-\sqrt{{2}}}}=\frac{{-{1}}}{{-\sqrt{{2}}}}=\frac{{1}}{\sqrt{{2}}}$

The slope of the line $\displaystyle\frac{{1}}{\sqrt{{2}}}.$

Find the inclination.

$\displaystyle\theta={\arctan{{\left(\frac{{1}}{\sqrt{{2}}}\right)}}}={{35.3}}^{\circ}={.6155}$ radians.

The inclination is 35.3 degrees or .6155 radians.

Notes