http://www.ck12.org Chapter 6. Analytic Trigonometry
6.4 Double, Half, and Power Reducing Identi-
ties
Here you will prove and use the double, half, and power reducing identities.
These identities are significantly more involved and less intuitive than previous identities. By practicing and working
with these advanced identities, your toolbox and fluency substituting and proving on your own will increase. Each
identity in this concept is named aptly. Double angles work on finding sin 80◦if you already know sin 40◦. Half
angles allow you to find sin 15◦if you already know sin 30◦. Power reducing identities allow you to find sin^215 ◦if
you know the sine and cosine of 30◦.
What is sin^215 ◦?
Watch This
MEDIA
Click image to the left for use the URL below.
URL: http://www.ck12.org/flx/render/embeddedobject/61324http://www.youtube.com/watch?v=-zhCYiHcVIE James Sousa: Double Angle Identities
MEDIA
Click image to the left for use the URL below.
URL: http://www.ck12.org/flx/render/embeddedobject/61326http://www.youtube.com/watch?v=Rp61qiglwfg James Sousa: Half Angle Identities
Guidance
The double angle identities are proved by applying the sum and difference identities. They are left as practice
problems. These are the double angle identities.
- sin 2x=2 sinxcosx
- cos 2x=cos^2 x−sin^2 x
• tan 2x= 1 2 tan−tanx (^2) x
The power reducing identities allow you to write a trigonometric function that is squared in terms of smaller
powers. The proofs are left as guided practice and practice problems.
- sin^2 x=^1 −cos 2 2 x