Five-Minute Check (over Lesson 13–3)
CCSS
Then/Now
Key Concept: Double-Angle Identities
Example 1: Double-Angle Identities
Example 2: Double-Angle Identities
Key Concept: Half-Angle Identities
Example 3: Half-Angle Identities
Example 4: Real-World Example: Simplify Using DoubleAngle Identities
Example 5: Verify Identities
Content Standards
F.TF.8 Prove the Pythagorean identity
sin2 (θ) + cos2 (θ) = 1 and use it to find sin (θ),
cos (θ), or tan (θ) given sin (θ), cos (θ), or
tan (θ) and the quadrant of the angle.
Mathematical Practices
3 Construct viable arguments and critique the
reasoning of others.
6 Attend to precision.
You found values of sine and cosine by using
sum and difference identities.
•  Find values of sine and cosine by using
double-angle identities.
•  Find values of sine and cosine by using
half-angle identities.
Double-Angle Identities
Find the value of cos 2! if sin=
between 0° and 90°.
and ! is
Find the value of cos 2! if sin! =
between 0° and 90°.
and ! is
Double-Angle Identities
A. Find the exact value of tan 2! if cos! =
! is between 0° and 90°.
and
Double-Angle Identities
B. Find the exact value of sin 2! if cos! =
! is between 0° and 90°.
and
Half-Angle Identities
A. Find
quadrant.
and ! is the second
Half-Angle Identities
B. Find the exact value of sin165!.
A. Find
quadrant.
and ! is in the fourth
B. Find the exact value of cos157.5!.
13.4 HW:
P. 897
12-32E