Applying Trigonometric Identities: Sum and Difference Formulas Big Idea: The following double angle trigonometric identities are printed in every Regents examination. There is no need to memorize them, but you should know when and how to use them.

Angle Sum Identities Functions of the Sum of Two Angles: Find the exact value of sin 105. We must use reference angles that we know. Tan (A + B) =

Angle Sum Identities Find the exact value of sin 105. We must use reference angles that we know.

Now find the exact value of cos105 Cos (60+45) = Cos60Cos45 –Sin60Sin45 = (½)(  2/2) - (  3/2) (  2/2) = (  2/4) – (  6/4) = (  2 -  6) 4

Functions of the Difference of Two Angles: Now use this example to figure out which identity to use the sum or difference: Cos(A-B) = cosACosB + SinASinB Tan (A-B) =

Functions of the Difference of Two Angles: Find the exact value of tan 135 Tan (180-45) = tan180-tan45 1+tan180tan45 = (0)(1) Tan (A-B)= ANSWER: -1 1

Cofunction Relationships of Acute Angles The “co” in cosine, cosecant, and cotangent signifies “complementary,” as in complementary angles (the measures of an angle and its complement sum to 90 degrees). Thus, acute angles and their complements are related as follows:

Negative Angle Identities  Sin(-A) = -sinA  Cos(-A) =Cos A  Tan(-A) = -tanA  Example: Sin (-45) = -Sin 45 Cos (-30) = cos 30

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