5-3 Tangent of Sums & Differences

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

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!!

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

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)

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

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!!)