ANGLES GREATER THAN 90 



25 



If we take a = 50, then sin a - 0-7660 ; but the sines of the 

 angles 180, 280, and 310 will all have this same numerical value. 



It must be noticed, however, that in each case the position 

 of the right-angled triangle is different, and therefore we have 

 to make allowance for that difference in position. 



If we take a reference circle and draw two diameters inclined 

 at an angle a to the horizontal diameter, then we can show the 

 triangle POR placed in its different positions with reference to 

 the circle ; obviously there is one triangle in each quadrant. 

 Let the radius of the circle always be positive. Taking the 



90' 



centre of the circle as origin and using the rule for positive and 

 negative quantities, as is usual in ordinary cases of plotting, then : 



Horizontal lines drawn to right of perpendicular diameter are +. 



Horizontal lines drawn to left of perpendicular diameter are . 



Perpendiculars drawn above the horizontal diameter are +. 



Perpendiculars drawn below the horizontal diameter are . 



We can now assign to the perpendicular and base of the right- 

 angled triangle POR the algebraic sign according to the position 

 with respect to the horizontal and vertical diameters. 



Tabulating the results : 



180 - a 180 + a 360 - a 



Hypotenuse OP 



Perpendicular PR 



Base OR 



Sine 



Cosine 



Tangent 



a 



+ 



+ 



+ 

 + 



