1. Warm Up Use trigonometric identities to simplify: csc ∙tan
cot ∙sin
Find the value of  in degrees (0°<  < 90°) and radians (0<  < π/2) w/o a calculator:
csc  = sec  =

2. 4.4 Trig Functions of Any Angle

3. Definitions of Trig Functions
Let  be an angle in standard position with (x, y) a point on the terminal side of  and Then…
sin  = y/r
csc  = r/y
cos  = x/r
sec  = r/x
tan  = y/x
cot  = x/y

4. Check this Out… - cos tan + sin cos tan + sin - sin cos - sin tan +II -
cos
tan +
sin
cos
tan +
sin -
sin
cos -
sin
tan +
tan +
cos IV
III

5. Example
Let (4, -3) be a point on the terminal side of  . Find the sin, cos and tan of  .
First we must find r. So r =
Therefore:
sin  = -3/5
cos  = 4/5
tan  = -3/4

6. EXAMPLE 2
Given cos = 3/5 and tan  < 0, find sin  and cot  .
Because the tan is negative and cos is positive, our answer is in quad___?
x = 3 and r = 5, we need to find y.
So… sin  = -4/5
cot = -3/4

7. Find the reference angle for the following angles
Reference Angles
If  is in standard position, then the reference angle  ́ is the acute angle formed by the terminal side of  and the x-axis.
EXAMPLE
Find the reference angle for the following angles
 = 125º
 = 5
 = -135º

8. More Examples… Evaluate each of the following: sin 210º cos (-5π/4)
tan (5π/3)
Let  be an angle in the third quadrant. Find:
sin 
tan 