ANALYTIC GKOM /.//;> 



v. 



angles are known, this equation determines tin- value of tin- 

 third. Thus this formula may be employed to determine 

 the slope of a line that shall make a given angle with a 

 given line. 



.</.. u r i\ -11 the line 3y 5x + 1 = 0, to find the equation 

 of a liiu- that shall make an angle of 60 with this linr. 

 Here <f> = b*0, t.e., tan< = V3, and if 6 l be the angk wliii-h 

 tin- L, r iven line makes with thr a^-axis, and 6^ that made by 

 tlu- lint- whose equation is sought, then tan B l f. Substi- 

 tuting these values in the above formula, it becomes 





whence 



i- the equation of a line fulfilling the required conditions, 

 k may be so determined that this line shall also pass 

 through any given point. 



It is to be remarked that through any given point there 

 may be drawn two lines, each of which shall make, with a 

 given line, an angle of any desired magnitude. 



E.g., through P l = (ar r ^j) the lines (1) and (2) may be 

 so drawn that each shall make an angle <p with the given 



