Page:Elements of the Differential and Integral Calculus - Granville - Revised.djvu/27

Rh $$\scriptstyle{x=\frac{x_1+x_2}{2},~y=\frac{y_1+y_2}{2}}$$; coördinates of middle point.

$$\scriptstyle{x=x_0+x',~y=y_0+y'}$$; transforming to new origin $$\scriptstyle{(x_0,y_0)}$$.

$$\scriptstyle{x=x'cos\theta-y'sin\theta,~y=x'sin\theta+y'cos\theta}$$; transforming to new axes making the angle $$\scriptstyle{\theta}$$ with old.

$$\scriptstyle{x=\rho\cos\theta,~y=\rho\sin\theta}$$; transforming from rectangular to polar coördinates.

$$\scriptstyle{\rho=\sqrt{x^2+y^2},~\theta=\operatorname{arc~tan}\frac{y}{x}}$$; transforming from polar to rectangular coördinates.

Different forms of equation of a straight line:

$$\scriptstyle{\tan\theta=\frac{m_1-m_2}{1+m_1m_2}}$$, angle between two lines whose slopes are $$\scriptstyle{m_1}$$ and $$\scriptstyle{m_2}$$. $$\scriptstyle{m_1=m_2}$$ when lines are parallel, and$$\scriptstyle{m_1=-\frac{1}{m_2}}$$ when lines are perpendicular.

$$\scriptstyle{(x-\alpha)^2+(y-\beta)^2=r^2}$$, equation of circle with center $$\scriptstyle{(\alpha,\beta)}$$ and radius $$\scriptstyle{r}$$.