Sum and Differences Of Periodic Functions Dr. Shildneck Spring, 2015
Derive the Cosine of a Difference Using the Unit Circle to Derive the Cosine of a Difference
Given two angles, u and v, we want to find a formula for the cosine of the difference between u and v. v θ = u - v u
θ
for the lengths of the two segments. θ θ = u - v Since , we can write an equivalence relation using the distance formula for the lengths of the two segments.
Derive the Cosine of a Sum Now… we can use the previous identity and the even/odd identities to Derive the Cosine of a Sum And…
Derive the Sine of a Sum and The Sine of a Difference Then… we can use the previous identities, co-function identities, and even/odd identities to Derive the Sine of a Sum and The Sine of a Difference And…
Derive the Tangent of a Sum and The Tangent of a Difference And then… we can use the previous identities, quotient identities, and even/odd identities to Derive the Tangent of a Sum and The Tangent of a Difference But… we aren’t going to… So, here are the rest…
SUM and DIFFERENCE IDENTITIES sin(1st)cos(2nd) [same operation] sin(2nd)cos(1st) cos(1st)cos(2nd) [opposite operation] sin(1st)sin(2nd)
Example 1 Find the exact value of C) Find the exact value of
Example 2 Find the exact value of
Example 3 Simplify the expression:
Example 4 Simplify the expression:
Example 5 Write as an expression of x.
Example 6 Find the exact value of if , in Quadrant 1 and in Quadrant 2.
ASSIGNMENT Assignment 2 WS