2.2 - Trigonometric Functions of Non-Acute Angles
Definition: Reference Angle  ' – the positive acute angle made by the terminal side of
an angle   and the x – axis.
QII  '  180  
QI  '  
QIII  '   180
QIV  '  360  
Ex: Find the reference angle for each angle.
1. 236 - Ref. angle = 236 – 180 = 56 
2. 1390 - Coterminal angle = 1390 – 3(360) = 310 
Ref. angle = 360 – 310 = 50 
Steps to find trig functions for any nonquadrantal  :
1. If   360 , or if   0 , find the coterminal  between 0 and 360
2. Find reference   '
3. Find trig function values for  '
4. Determine correct signs for values based on quadrant where  is located.
Ex: Find the exact values of each of the following without the use of a calculator.
3. sin 210 - Ref. angle = 210 – 180 = 30 
sin 30  = ½
sin 210  = - ½
4. cos 240 - Coterminal angle = -240 + 360 = 120 
Ref. angle = 180 – 120 = 60 
cos 60  = ½
cos (-240  ) = - ½
5. tan 675 - Coterminal angle = 675 – 360 = 315 
Ref. angle = 360 – 315 = 45 
tan 45  = 1
tan 675  = -1