# Objective- Evaluate trigonometric functions of any angle

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```					Objective- Evaluate trigonometric functions of
any angle.

y
(x, y)

r
x

r  x y2       2
Six Trigonometric Functions

y               y
r
sin          (x, y)           csc  
r                              y
r
x                                 r
cos                             sec  
r                       x
x

y                               x
tan                           cot  
x                               y
Evaluate the six trigonometric functions.

y                     3               4
(-4, 3)             sin         cos   
5               5

3         5
r                 tan      csc  
4         3
x
r 5                            5             4
sec        cot   
4             3
If the terminal side of  lies on a axis,
then  is a quadrantal angle.
y

  0
(r, 0)   x

xr
y0
If the terminal side of  lies on a axis,
then  is a quadrantal angle.
y
(0, r)
x0
yr
  90
x
If the terminal side of  lies on a axis,
then  is a quadrantal angle.
y

(-r, 0)            180
x
x  r
y0
If the terminal side of  lies on a axis,
then  is a quadrantal angle.
y

  270
x
x0
y  r                      (0, -r)
Evaluate the six trigonometric functions of
  90
x  0, y  r

y y                          x 0
sin     1                cos     0
r y                          r r
y y                          r r
tan     undefined        csc     1
x 0                          y r
r r                          x 0
sec   = = undefined        cot     0
x 0                          y y
Reference Angle
y


   '

x

Reference Angle- is the acute angle  formed
'

by the terminal side of  and the x-axis.
Find the reference  for each angle  .
'

1. 310                      2
4.
  360  310
'
3
2 
  50
'
  
'

3 3
6
2. 170                5.
5
  180 170
'
6      
  10
'                     
'

7  5      5
3. 200                6.
4
  200 180
'                          7 
  2 
'

  20
'
4 4
1. Evaluate cos225
  225 180  45 Quadrant III
2

2. Evaluate tan120            2

  180 120  60 Quadrant II

11           3
3. Evaluate sin