Download 7-4 Notes

Section 7­4.notebook
December 16, 2016
Sec. 7.4 Double Angle & Half­Angle Identites
Find an expression for sin 2θ
Find an expression for cos 2θ
Mar 17­8:41 AM
Double Angle Identities:
1. sin 2θ = 2sinθcosθ
2. cos 2θ = cos2θ - sin2θ
(you can get other variations of this if
you substitute 1 - cos2θ in for sin2θ and
1 - sin2θ in for cos2θ)
Nov 12­8:46 AM
What was your favorite cartoon when you were younger?
3. tan 2θ = 2tanθ
1 - tan2θ
Jan 20­11:09 AM
Dec 15­7:50 AM
Examples:
Find the exact value of each function if sin θ = 3/4 and the terminal side of θ is in Quad. I
a.) sin 2θ
b.) cos 2θ
Half Angle Identities:
1. sin α/2 = ±√((1­cosα)/2)
2. cos α/2 = ±√((1+cosα)/2)
c.) tan 2θ
3. tan α/2 = ±√((1 ­ cos α)/(1 + cosα)) where cos α ≠ ­1
Nov 12­9:03 AM
Jan 20­11:14 AM
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Section 7­4.notebook
December 16, 2016
Examples:
Use a Half­Angle identity to find the exact value of tan 15o
Verify that cos 2x = cot x ­ 1 1 + sin 2x cot x + 1
Use a Half­Angle identity to find the exact value of cos π
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Nov 13­3:27 PM
Verify 1 ­ cos 2xsec2x = tan2x
Nov 13­3:33 PM
Assignment: Sec. 7.4 p. 454 #16, 21­27 (odds), 34, 40, 44
• I can use algebraic manipulation and established trigonometric identities to verify other trigonometric identities.
Nov 13­3:43 PM
Apr 17­2:46 PM
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