10-2

This week we’ve learned several sections of Chapter 10. In section 10-2, we were introduced to tangent formulas. In this section, the objective was to derive and apply formulas for tan (alpha +/- beta).
Sum Formula:
tan (alpha + beta) = tan alpha + tan beta / 1 – tan alpha * tan beta

Difference Formula:
tan (alpha – beta) = tan alpha – tan beta / 1 + tan alpha * tan beta

EXAMPLE 1: Simplify, tan 120 degrees – tan 60 degrees/ 1 + tan 120 degrees tan 60 degrees
A). According to the sum/difference formulas, this is a difference formula.
B). Replace the right side with the left.
C). tan (120 degrees – 60 degrees)
D). tan 60 degrees is in your trig chart. So, your final answer is square root of 3.

EXAMPLE 2: Suppose tan alpha = -1/2 and tan beta = 1/3. Find tan (alpha + beta).
A). Since the problem asks you to find the sum, use the sum formula.
B). Replace the left side with the right and plug in your alpha and beta.
C). -1/2 + 1/3 / 1 – (-1/2)(1/3)
D). -1/7 is your answer.