1. Double and Half Angle Formulas
Dr. Barry Shildneck

2. Double Angle Formulas
Given that you know the sum and difference formulas, derive a formula for the Sine, Cosine, and Tangent of twice an angle.

3. sin(1st)cos(2nd) [same op] sin(2nd)cos(1st)
cos(1st)cos(2nd) [opposite op] sin(1st)sin(2nd)
Note: You do not have to remember the tangent formula if you just remember the quotient identities.

4. Example: Derive the formula for
Question: What does “2x” mean?
2x =
(2)(x)=
x + x
So what does the sin(2x) equal?:
sin(2x)=
sin(x + x)

5. Deriving sin(2x) sin(2x)= sin(x + x) = sin(x)cos(x) + sin(x)cos(x)

6. Deriving tan(2x)

7. Deriving Cos(2x) OR OR

8. Double Angle Formulas Note:
The sign of the value of the double angle is taken care of by the formula.

9. Example 1 sin(2θ) cos(2θ) tan(2θ) csc(2θ) cot(2θ)
Use the triangle to determine the
Values of each of the following.
sin(2θ)
cos(2θ)
tan(2θ)
csc(2θ)
cot(2θ)

10. Example 2
Find the values of the cos2x given

11. Example 3
Use identities to rewrite each expression in terms of a single trigonometric function.
1) 4sinxcosx
2) 5–10cos2x

12. Sinus Minus Cosine Snot
Half Angle Formulas
Sinus Minus
Cosine Snot

13. Example 4
Use the half-angle formula to find the exact value of the sin112.5o.

14. Example 5
Given , find the value of .

15. Assignment
Assignment 10 – Multiple and Half Angle Identities Worksheet