March 13, 2017
Problem 5.3
Name: __________________
Using the sum or difference formulas, find the exact value.
cos 75o
_____________
March 13, 2017
Problem 5.3
Name: __________________
Using the sum or difference formulas, find the exact value.
cos 75o =
cos(45o + 30o) = cos45o cos30o - sin45o sin30o
=
=
=
√3
√2
2
2
6
4
-
6-2
4
√2
2
2
4
1
2
March 13, 2017
March 13, 2017
(5.4) Multiple-Angle Identities
Objective: To learn the Double-Angle Identities.
Why: These identities will be used in calculus.
March 13, 2017
Obj: To learn the Double-Angle Identities, Power-Reducing
Identities, and Half-Angle Identies.
Double Angle Identities
sin 2u
=
cos 2u =
tan 2u
2 sin u cos u
2
2
cos u - sin u
2
=
2cos u - 1
=
1 - 2sin u
=
2
2 tan u
2
1 - tan u
March 13, 2017
Obj: To learn the Double-Angle Identities, Power-Reducing
Identities, and Half-Angle Identies.
1. Use the sum and difference formulas to prove the identity.
sin 2u = 2 sin u cos u
March 13, 2017
Obj: To learn the Double-Angle Identities, Power-Reducing
Identities, and Half-Angle Identies.
2. Use the sum and difference formulas to prove the identity.
cos 2u = 2cos2u - 1
March 13, 2017
Obj: To learn the Double-Angle Identities, Power-Reducing
Identities, and Half-Angle Identies.
3. Find all solutions in the interval [0, 2
2 cos x + sin 2x = 0
)
March 13, 2017
4.
cos 2x
= sin x
Obj: To learn the Double-Angle Identities, Power-Reducing
Identities, and Half-Angle Identies.
March 13, 2017
HW:
(5.4) Pg.432: 5, 7, 8, 23, 24
Obj: To learn the Double-Angle Identities, Power-Reducing
Identities, and Half-Angle Identies.