1. DOUBLE-ANGLE AND HALF-ANGLE FORMULAS

2. If we want to know a formula for we could use the sum formula.
we can trade these places
This is called the double angle formula for sine since it tells you the sine of double 

3. Let's try the same thing for
This is the double angle formula for cosine but by substiuting some identities we can express it in a couple other ways.

4. Double-angle Formula for Tangent

5. Summary of Double-Angle Formulas

6. We can also derive formulas for an angle divided by 2.
Half-Angle Formulas
As stated it is NOT both + and - but you must figure out where the terminal side of the angle is and put on the appropriate sign for that quadrant.

8. We could find sin 15° using the half angle formula.
30°
30°
Since 15° is half of 30° we could use this formula if  = 30°
15° is in first quadrant and sine is positive there so we want the +

9. Let's draw a picture. 5 4   -3
Use triangle to find values.

10. If  is in quadrant II then half  would be in quadrant I where sine is positive5 4   -3
Use triangle to find cosine value.

11. Acknowledgement
I wish to thank Shawna Haider from Salt Lake Community College, Utah USA for her hard work in creating this PowerPoint.
Shawna has kindly given permission for this resource to be downloaded from and for it to be modified to suit the Western Australian Mathematics Curriculum.
Stephen Corcoran
Head of Mathematics
St Stephen’s School – Carramar