Download PCH Notes 5.4a

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5.4(a) Notes: Sum and Difference Formulas
Lesson Objective: Use sum and difference
formulas to evaluate trig functions and verify
identities.
CCSS: F-TF Extend the domain of trigonometric
functions using the unit circle.
You will need: your trig identities cheat sheet
Lesson 1: Cosine of the Sum of 2 Angles
Use a graphing utility to graph y1 = cos(x + 2)
and y2 = cos x + cos 2 in the same viewing
window. What can you conclude about the
graphs? Is it true that cos(x + 2) = cos x + cos 2?
Lesson 1: Cosine of the Sum of 2 Angles
1. cos(u + v) = cos u cos v – sin u sin v
Derived from the distance formula (see p. 424
for the proof); can be used to find the exact
value of the cosine of any angle.
Lesson 1: Cosine of the Sum of 2 Angles
1. cos(u + v) = cos u cos v – sin u sin v
Derived from the distance formula (see p. 424
for the proof); can be used to find the exact
value of the cosine of any angle.
How can we remember this formula? There will
actually be 5 more to add to this one.
Lesson 1: Cosine of the Sum of 2 Angles
1. cos(u + v) = cos u cos v – sin u sin v
Find the exact value of cos 105°.
Lesson 2: The Rest of the Sum & Diff Formulas
1. cos(u + v) = cos u cos v – sin u sin v
2. cos(u – v) = cos u cos v + sin u sin v
Lesson 2: The Rest of the Sum & Diff Formulas
1. cos(u + v) = cos u cos v – sin u sin v
2. cos(u – v) = cos u cos v + sin u sin v
3. sin(u + v) = sin u cos v + cos u sin v
4. sin(u – v) = sin u cos v – cos u sin v
Lesson 2: The Rest of the Sum & Diff Formulas
1. cos(u + v) = cos u cos v – sin u sin v
2. cos(u – v) = cos u cos v + sin u sin v
3. sin(u + v) = sin u cos v + cos u sin v
4. sin(u – v) = sin u cos v – cos u sin v
5. tan(u + v) = tan u + tan v
1 – tan u tan v
6. tan(u – v) = tan u – tan v
1 + tan u tan v
Lesson 3: Evaluating a Trig Expression
Find the exact value of sin
5π
.
12
Lesson 4: Evaluating a Trig Expression
Find the exact value of cot(u + v) given sin u =
and cos v = -
3
,
5
where both angles are in QII.
5
13
Lesson 5: Finding the Exact Value in Reverse
Find the exact value.
A. cos 70° cos 40° + sin70° sin 40°
Lesson 5: Finding the Exact Value in Reverse
Find the exact value.
B. sin 3x cos 2y + cos 3x sin 2y
5.4(a): Do I Get It? Yes or No
Find the exact value.
1. cos 75°
π
2. sin
12
3. Find the exact value of csc(u – v) given sin u
5
3
= and cos v = - , where both angles are
13
5
in QII.
4. sin 42° cos 12° – cos 42° sin 12°
5. cos 3 cos 1.2 – sin 3 sin 1.2