CH 10.7 Double Angle and Half Angle Formulas ... AWS
CH 10.7 Double Angle and Half Angle Formulas.notebook
May 07, 2012
Apply DoubleAngle and Half Angle Formulas
There are formulas not just for adding angles as we saw with the sum and difference formulas, there are also formulas for multiplying angles.
1
CH 10.7 Double Angle and Half Angle Formulas.notebook
May 07, 2012
Apply DoubleAngle and Half Angle Formulas Double Angle Formula for Sine
2
CH 10.7 Double Angle and Half Angle Formulas.notebook
May 07, 2012
Apply DoubleAngle and Half Angle Formulas Double Angle Formula for Cosine
3
CH 10.7 Double Angle and Half Angle Formulas.notebook
May 07, 2012
Apply DoubleAngle and Half Angle Formulas Double Angle Formula for Tangent
4
CH 10.7 Double Angle and Half Angle Formulas.notebook
May 07, 2012
Apply DoubleAngle and Half Angle Formulas Half Angle Formula for Sine
5
CH 10.7 Double Angle and Half Angle Formulas.notebook
May 07, 2012
Apply DoubleAngle and Half Angle Formulas Half Angle Formula for Cosine
6
CH 10.7 Double Angle and Half Angle Formulas.notebook
May 07, 2012
Apply DoubleAngle and Half Angle Formulas Half Angle Formula for Tangent
7
CH 10.7 Double Angle and Half Angle Formulas.notebook
May 07, 2012
Apply DoubleAngle and Half Angle Formulas
Solve:
8
CH 10.7 Double Angle and Half Angle Formulas.notebook
May 07, 2012
Apply DoubleAngle and Half Angle Formulas
Since: Substitute:
9
CH 10.7 Double Angle and Half Angle Formulas.notebook
May 07, 2012
Apply DoubleAngle and Half Angle Formulas
Factor out cos(θ)
10
CH 10.7 Double Angle and Half Angle Formulas.notebook
May 07, 2012
Apply DoubleAngle and Half Angle Formulas Solve the cosine portion of the equation.
or
11
CH 10.7 Double Angle and Half Angle Formulas.notebook
May 07, 2012
Apply DoubleAngle and Half Angle Formulas
Solve the sine portion of the equation.
12
CH 10.7 Double Angle and Half Angle Formulas.notebook
May 07, 2012
Apply DoubleAngle and Half Angle Formulas
Solve:
13
CH 10.7 Double Angle and Half Angle Formulas.notebook
May 07, 2012
Apply DoubleAngle and Half Angle Formulas
Choose a double angle cosine formula:
14
CH 10.7 Double Angle and Half Angle Formulas.notebook
May 07, 2012
Apply DoubleAngle and Half Angle Formulas
Since: Substitute:
15
CH 10.7 Double Angle and Half Angle Formulas.notebook
May 07, 2012
Apply DoubleAngle and Half Angle Formulas
Now use the Quadratic Formula
16
CH 10.7 Double Angle and Half Angle Formulas.notebook
May 07, 2012
Apply DoubleAngle and Half Angle Formulas
17
CH 10.7 Double Angle and Half Angle Formulas.notebook
May 07, 2012
Apply DoubleAngle and Half Angle Formulas
18
CH 10.7 Double Angle and Half Angle Formulas.notebook
May 07, 2012
Apply DoubleAngle and Half Angle Formulas
19
Attachments
CH 10.7 Sketches.gsp
May 07, 2012
Apply DoubleAngle and Half Angle Formulas
There are formulas not just for adding angles as we saw with the sum and difference formulas, there are also formulas for multiplying angles.
1
CH 10.7 Double Angle and Half Angle Formulas.notebook
May 07, 2012
Apply DoubleAngle and Half Angle Formulas Double Angle Formula for Sine
2
CH 10.7 Double Angle and Half Angle Formulas.notebook
May 07, 2012
Apply DoubleAngle and Half Angle Formulas Double Angle Formula for Cosine
3
CH 10.7 Double Angle and Half Angle Formulas.notebook
May 07, 2012
Apply DoubleAngle and Half Angle Formulas Double Angle Formula for Tangent
4
CH 10.7 Double Angle and Half Angle Formulas.notebook
May 07, 2012
Apply DoubleAngle and Half Angle Formulas Half Angle Formula for Sine
5
CH 10.7 Double Angle and Half Angle Formulas.notebook
May 07, 2012
Apply DoubleAngle and Half Angle Formulas Half Angle Formula for Cosine
6
CH 10.7 Double Angle and Half Angle Formulas.notebook
May 07, 2012
Apply DoubleAngle and Half Angle Formulas Half Angle Formula for Tangent
7
CH 10.7 Double Angle and Half Angle Formulas.notebook
May 07, 2012
Apply DoubleAngle and Half Angle Formulas
Solve:
8
CH 10.7 Double Angle and Half Angle Formulas.notebook
May 07, 2012
Apply DoubleAngle and Half Angle Formulas
Since: Substitute:
9
CH 10.7 Double Angle and Half Angle Formulas.notebook
May 07, 2012
Apply DoubleAngle and Half Angle Formulas
Factor out cos(θ)
10
CH 10.7 Double Angle and Half Angle Formulas.notebook
May 07, 2012
Apply DoubleAngle and Half Angle Formulas Solve the cosine portion of the equation.
or
11
CH 10.7 Double Angle and Half Angle Formulas.notebook
May 07, 2012
Apply DoubleAngle and Half Angle Formulas
Solve the sine portion of the equation.
12
CH 10.7 Double Angle and Half Angle Formulas.notebook
May 07, 2012
Apply DoubleAngle and Half Angle Formulas
Solve:
13
CH 10.7 Double Angle and Half Angle Formulas.notebook
May 07, 2012
Apply DoubleAngle and Half Angle Formulas
Choose a double angle cosine formula:
14
CH 10.7 Double Angle and Half Angle Formulas.notebook
May 07, 2012
Apply DoubleAngle and Half Angle Formulas
Since: Substitute:
15
CH 10.7 Double Angle and Half Angle Formulas.notebook
May 07, 2012
Apply DoubleAngle and Half Angle Formulas
Now use the Quadratic Formula
16
CH 10.7 Double Angle and Half Angle Formulas.notebook
May 07, 2012
Apply DoubleAngle and Half Angle Formulas
17
CH 10.7 Double Angle and Half Angle Formulas.notebook
May 07, 2012
Apply DoubleAngle and Half Angle Formulas
18
CH 10.7 Double Angle and Half Angle Formulas.notebook
May 07, 2012
Apply DoubleAngle and Half Angle Formulas
19
Attachments
CH 10.7 Sketches.gsp
