1. The Circular Functions (14.2)

2. A reference angle, ’, is the smallest, positive degree measure from the terminal side to the x-axis.
(x, y) r  ’
Use Pythagorean Theorem:
x2 + y2 = r2
Note: x can be  and y can be  (depending on the Quadrant)
Since r is the radius, it must be (+) because it is a length.

3. I. The Six Trigonometric Functions
Cosine:
cos  = x
Secant:
sec  = r r x
Sine:
sin  = y
Cosecant:
csc  = r r y
Tangent:
tan  = y
Cotangent:
cot  = x y x

4. II. Sine and Cosine
If the terminal ray of angle  in standard position contains (x, y) on the unit circle, then cos  = x and sin  = y or (cos , sin ) = (x, y).
b/c radius is always 1
-1 ≤ cos  ≤ 1 and -1 ≤ sin  ≤ 1
Look at x-values and y-values so far on the unit circle

5. A. Finding trig values using calculator:
Example:
Use a calculator. Round to the nearest four decimal places.
a) Sin 45° 
.7071
b) cos 20° 
.9397
sin 45
enter
cos 20
enter
NOTE: Make sure your calculator is in degree mode.

6. B. Finding angles using trig values and a calculator:
Example:
If 0 <  < 90, what is ? Round angles to the nearest tenth.
a) sin  
b) cos  
2nd
sin
.5299
enter
You’re “undoing” sine
 = 32.0
2nd
cos
.7218
enter
 = 43.8
NOTE: Make sure your calculator is in degree mode.

7. I. The Six Trigonometric Functions
Cosine:
cos  = x
Secant:
sec  = r = r x
cos 
Sine:
sin  = y
Cosecant:
csc  = r = r y
sin 
Tangent:
tan  = y
= sin 
Cotangent:
cot  = x
= cos  x
cos  y
sin 

8. III. Using all Trig Functions