Double Angle and Half Angle Formula

Review Double & Half Angle Identities

Multiple Choice

sin2u =

• (sinu)(cosu)

• 2(sinu)(cosu)

• (sinu)^2

• 2(sinu)^2

Multiple Choice

Use a double-angle identity to find the exact value of each expression
cos θ = 4/5 and 270° < θ < 360°
Find sin 2θ

• -1/5

• 24/25

• -24/25

• -25/24

Multiple Choice

Use the information about the angle θ, 0≤θ<2π to find the exact value of
sin (2θ)
1. sin θ= 3/5 , 0<θ<π/2

• 24/7

• 7/25

• 24/25

• 1/2

Multiple Choice

Find the exact value of sin 2x if sin x = 12/13 and x is in the first quadrant. 

• 120/169

• 25/169

• 60/169

• 5/13

Multiple Choice

Using the second identity, find Cos(50)

• sin²(25) - cos²(25) 

• cos²(50) - sin²(50)

• cos²(25) - sin²(25)

• sin²(50) - cos²(50) 

Multiple Choice

Using the third identity, find Cos(40)

• 2cos² (40) - 1

• 2cos² (20) - 1

• 2cos² (20) + 1

• 2cos² (40) + 1

Multiple Choice

Use a double-angle or half-angle identity to find the exact value of each expression
sin θ = −3/5 and 3π/2 < θ < 2π Find tan θ/2

• -1/3

• -√3

• √3/3

• -1

Multiple Choice

Use the Half-angle formulas to find the exact value of each expression
sin 22.5º

• √(2 + √3)/2

• √(2 - √2)/2

• √(2 + √2)/2

• √(2 - √3)/2

Multiple Choice

If $$\cos A=\frac{1}{3}$$  , then the positive value of  $$\tan\ \frac{A}{2}$$  ?

• $$\sqrt{2}$$  

• $$\sqrt{3}$$  

• $$\frac{\sqrt{3}}{3}$$  

• $$\frac{\sqrt{2}}{2}$$  

Multiple Choice

If $$\cos\theta=\frac{1}{8},$$  the positive value of  $$\sin\ \frac{\theta}{2}$$  is

• $$\frac{3}{2}$$  

• $$\frac{\sqrt{7}}{4}$$  

• $$\frac{9}{16}$$  

• $$\frac{3}{4}$$  

Multiple Choice

The expression $$2\sin30^o\cos30^o$$  has the same value as

• $$\sin15^o$$  

• $$\cos60^o$$  

• $$\sin60^o$$  

• $$\cos15^o$$  

Multiple Choice

If $$\cos\theta=\frac{1}{8},$$  what is the value of  $$\sin\ \frac{\theta}{2}$$  if $$\frac{3\pi}{2}<\theta<2\pi$$  

• $$\frac{3}{2}$$  

• $$-\frac{\sqrt{7}}{4}$$  

• $$\frac{9}{16}$$  

• $$-\frac{3}{4}$$  

Multiple Choice

Use a double angle identity to find the exact value of  $$\sin420\degree$$  

• $$-1$$  

• 0

• $$\frac{1}{2}$$  

• $$\frac{\sqrt{3}}{2}$$  

Poll

After this review, I feel ------------ about using double & half angle identities

• very confident

• confident/OK

• shaky...I'm so-so

• not so sure...I'm very confused

• Other: my thoughts/feelings are not expressed here