1. 5-3 Tangent of Sums & Differences

2. 5-3 Tangent of Sums & Differences
Derive formulas for tangents of sums & differences
Use sums & differences of tangents to simplify expressions
Use sums & differences of tangents to solve Trig. Equations

3. Tangent Using sine & cosine
Recall tangent can be expressed as tan  = sin 
cos 
Using sine & cosine of sums (or differences)
tan ( ) = sin ( ) = sin  cos   cos  sin
cos ( ) cos  cos   sin  sin
Dividing each term by cos  cos  you obtain
tan ( ) = sin  cos   cos  sin
cos  cos  cos  cos 
cos  cos   sin  sin
cos  cos  cos  cos 
Simplifying tan ( ) = tan   tan 
1  tan  tan 
Note: The signs on the top are the same but signs on the bottom are opposites!!

4. Ex 1 Use a sum or difference to find an exact value
tan (15°)
tan (-5p/12)

5. Ex 2 Write the expression as the tangent of an angle
tan 21° + tan 36°
1 – tan 21° tan 36°
tan (2p/5) – tan (p/3)
1 + tan (2p/5) tan (p/3)

6. Ex 3 Prove the identity tan (x + y) tan (x – y) = tan2 x – tan2 y
tan (p/2 – u) = cot u

7. Group Work – Exit Ticket
Discuss each of the following and submit to the turn in box BEFORE you exit class
#64, 65, and 71* (Challenging but you can do it!!)