1. Trigonometry
Identities

2. Right Triangle SOHCAHTOA Hypotenuse Side opposite to  
Side adjacent to 

3. Examples Find exact values for all trig function in this triangle: 5 4 3

4. Sines, Cosines, Tangents of Special Angles

5. Cofunctions sin (90˚ - ) = cos  cos (90˚ - ) = sin 
Ex. sin 52 ˚ = cos 48 ˚ =
tan (90˚ - ) = cot  cot (90˚ - ) = tan 
Ex. tan 13 ˚= cot 77 ˚ =
sec (90˚ - ) = csc  csc (90˚ - ) = sec 
Ex. sec 43 ˚= csc 47 ˚ =

6. Fundamental Trig Identities
Reciprocal Identities
Quotient Identities

7. Pythagorean Identities
(cos , sin ) 1
sin 
cos 
sin 2  + cos 2  = 1

8. Pythagorean Identities
cos 2  + sin 2  = 1
sin 2  sin 2  sin 2 
cot 2  = csc 2 
cos 2  cos 2  cos 2 
tan 2  = sec 2 

9. Using Trig Identities Simplify: sin  csc  1 Simplify: tan  cos 
(csc  + cot ) (csc  - cot )
csc 2  - cot 2  1

10. Using a Calculator Find the csc 46.89˚
The calculator does not have csc, so we must use
the reciprocal identity

11. Applications

12. Applications
An historic lighthouse is 200 yards from a bike path along the edge of a lake. A walkway to the lighthouse is 400 yards long. Find the acute angle  between the bike path and the walkway.
 = 30˚

13. Applications
Find the length of a skateboard ramp if the angle from the ground is 18.4˚ and the vertical side is 4 feet high.
Ramp = 12.7 ft