Transcript Ch.7 Sec.4

Ch.7 Sec.4
Double Angle and Half Angle
Formulas
sin(2Θ)
• Use the sum formula for sines to find an
identity.
• Do the same thing for cos(2Θ)
Theorem Double-Angle Formulas
Ex:
• Suppose sin(Θ)=2/3 and Θ has its terminal
side in the first quadrant, find the exact
value of each function.
• a. sin(2Θ)
• b. cos(2Θ)
• c. tan(2Θ)
• d. cos(4Θ)
Theorem Half-Angle Formulas
where the + or - sign is determined by the
quadrant of the angle
Use a half-angle identity to find the
exact value of each function.
• a. sin(7pi/12)
• b. Cos(67.5)
Last One!
• Verify that …
cos(2 )
cot( )  1

1  sin(2 ) cot( )  1