February 23, 2017
February 23, 2017
(5.3) Sum and Difference Identities
Objective: To learn the sum and difference trigonometric identities.
Why: These identities provide clear examples of how different
the algebra of functions can be different than the algebra of
real numbers.
February 23, 2017
Sum and Difference Identities
Obj: To learn the sum and difference trigonometric identities.
sin(u + v) = sinu cosv + cosu sinv
sin(u - v) = sinu cosv - cosu sinv
cos(u + v) = cosu cosv - sinu sinv
cos(u - v) = cosu cosv + sinu sinv
tan(u + v) =
tan(u - v) =
tanu + tanv
1 - tanu tanv
tanu - tanv
1 + tanu tanv
February 23, 2017
Unit Circle
(cosu, sinu)
u
February 23, 2017
Obj: To learn the sum and difference trigonometric identities.
Identify the trigonometric identity used. Then write the expression as the sine,
cosine, or tangent of an angle.
o
o
o
1. cos94 cos18 +sin94 sin18
2. tan 3x - tan 2y
1 + tan 3x tan 2y
o
February 23, 2017
Obj: To learn the sum and difference trigonometric identities.
Examples. Simplify.
1. sin( π - x )
February 23, 2017
Obj: To learn the sum and difference trigonometric identities.
2. Confirm the cofunction identity.
cos(
π
2
-x)
= sin x
February 23, 2017
Obj: To learn the sum and difference trigonometric identities.
o
3. Find the exact value of sin 15 .
February 23, 2017
Obj: To learn the sum and difference trigonometric identities.
4. Find the exact value of tan
7π
12
.
February 23, 2017
Obj: To learn the sum and difference trigonometric identities.
5. Find the exact value of sin(u + v) given:
sin u =
cos v =
4
5
-12
13
and
0<u<
π
2
and
π
2
<v<
π
February 23, 2017
Obj: To learn the sum and difference trigonometric identities.
HF:
(HR) Pg.425: 1-9odd, 25, 27, 37, 47, 49