Double­Argument & Half­Argument Properties
7.5 ﴾Day 1﴿ Double­angle and Half­angle Formulas ­ Notes
sin (2A)=
Goal #3
formula for tan 2A
tan(2A)=
cos(2A)=
1
Double­Argument & Half­Argument Properties
Double‐Argument (Double‐Angle) Properties
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Double­Argument & Half­Argument Properties
3
Double­Argument & Half­Argument Properties
Half Argument
Properties
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Double­Argument & Half­Argument Properties
Use the information given about the angle θ, 0 ≤ θ ≤ 2π, to find the exact value of:
(i) sin (2θ) (ii) cos (2θ) (iii) (iv) cos 2A = cos2A ­ sin2A
cos 2A = 1 ­ 2 sin2A
cos 2A = 2 cos2A ­ 1
sin 2A = 2 sin A cos A
A)
(i) sin (2θ) (ii) cos (2θ) (iii) (iv) Use the Half‐ angle Formula to find the exact value of each expression.
B) cos 15o
C) sin (­15o)
D)
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Double­Argument & Half­Argument Properties
Draw and label diagrams. Find the exact value of each expression:
cos 2A = cos2A ­ sin2A
cos 2A = 1 ­ 2 sin2A
cos 2A = 2 cos2A ­ 1
sin 2A = 2 sin A cos A
E)
F)
G)
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