Double-Angle and Half-Angle Identities

​Please take a moment and look at the Double-Angle and Half-Angle Identities in your flipchart.

Please watch the video and take notes in your INB.​

Multiple Choice

cos 2x =

• 2 sin x cos x

• cos²x - sin²x

• 2 cos²x - 2

• sin²x - cos²x

Multiple Choice

Which identity represents a double-angle identity for sin 2θ?

• 2sinθcosθ
• cos²θ - sin²θ
• 1 - 2sin²θ
• 2cos²θ - 1

Multiple Select

Select all that represent a double-angle identity for cos 2θ?

• 2sinθcosθ
• cos²θ - sin²θ
• 1 - 2sin²θ
• 2cos²θ - 1

Multiple Choice

cos 2x =

• 2(sin x)(cos x)

• $$\cos^2x+\sin^2x$$  

• $$2\cos^2x-1$$  

• $$\sin^2x-\cos^2x$$  

​Copy the examples from the next video in your INB. Feel free to pause and try some of the questions on your own.

Multiple Choice

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

• $$\sin15^o$$  

• $$\cos60^o$$  

• $$\sin60^o$$  

• $$\cos15^o$$  

Multiple Choice

The expression $$10\sin2x\cos2x$$  has the same value as

• $$\sin20x$$  

• $$\cos20x$$  

• $$5\ \sin4x$$  

• $$4\ \sin\ 5x$$  

Multiple Choice

The expression $$\cos^2\ 23°\ -\ \sin^2\ 23°$$  has the same value as

• $$\sin32°$$  

• $$\cos64°$$  

• $$\cos\ 46°$$  

• $$\sin\ 46°\ \cos\ 46°$$  

Multiple Choice

The expression $$2\cos^2\ 22.5°\ -\ 1$$  has the same value as

• $$\sin\ 45°$$  

• $$\cos45°$$  

• $$\cos\ \left(\frac{22.5}{2}\right)°$$  

• $$\cos\ 22.5°$$  

​Watch the video on the next slide and copy the notes into your INB.

Multiple Choice

Use a double-angle or half-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 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

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

If $$\sin\theta=\frac{\sqrt{5}}{3}$$  , then  $$\cos2\theta$$  equals

• $$\frac{1}{3}$$  

• $$-\frac{1}{3}$$  

• $$\frac{1}{9}$$  

• $$-\frac{1}{9}$$  

​Watch the video on the next slide and copy the notes into your INB.

Please try the problem to your right. The answers are on the next page.​

​

​Please complete the worksheet attached in the assignment tab.