Download Sec 4.3 Notes (Trig Ratios of Any Angle) - 2013

Name: ________________________________________
Pre-Calculus
Date __________________________________________
Period: _____________
Section 4.3 Notes Trig Ratios of ANY Angle
Def. of Angle
(Geometry)
Def. of Angle
(Trigonometry)
Initial Side
Terminal Side
Coterminal
Angles
Ex 1
Find a negative and positive co-terminal angle for each of the
following:
a) 45˚

b)
9
c) –372˚
Reference
Triangle
Name: ________________________________________
Pre-Calculus
Date __________________________________________
Period: _____________
Definitions of
Trig. Ratios
Ex 2
Point P is on the terminal side of angle  . Evaluate all 6 trig
functions for  .
a) P(4, 7)
b) P(–4, 2)
c) P(0, 6)
Quadrantal
Angles
Periodic
Function
Ex 3
Find each of the following trig ratios without a calculator.
a) cos(1845Þ)
 5200 
sin 
 4 
b)
 13 
c) tan 
 6 
Name: ________________________________________
Pre-Calculus
Date __________________________________________
Period: _____________
Ex 4
Find cot  if cos 
1
(how many answers are there?)
4
Ex 5
For each of the following scenarios, determine which of the 6 trig
Determine if
ratios are positive? negative? Zero?
ratios are + or –
a. If 0    90Þ
b. If

2
  
 3 
c. If  is in the interval   , 

2 
  
d. If  is in the interval   ,0 
 2 
Ex 6
Find sec and csc if cot   
4
and sin  0
3
Name: ________________________________________
Pre-Calculus
Date __________________________________________
Period: _____________
Given a circle with a radius of 1 and center of (0,0). Angles in first quadrant are
  
, , .
6 4 3
All other angles are reflections of angles in the first quadrant.
(1,0)
0˚, 0 radian
Try on your own (without calculator)
 7 
 11 
cos 
sin 

 4 
 6 
 3 
tan  
 4 
sec  
 5 
csc 
 3 

cot  
 3