Exam Review:
Compound & Double angle formula
By:Antonio Jajou & Marwan Abuseir
7.2- Compound Angle Formulas
7.3 Double Angles
Things you need to know
- Double angle Formula- The formulas shows that there is a relationship between the trigonometric ratio for a double angle to the trigonometric ratios the original angle.
- The Double angle formula can be obtain from the appropriate compound angle formulas.
- It can be used to simplify expressions and solve for exact values. This can also be used to develop other equivalent formulas.
- To recognize which formula to use looking at the question.
- To be able to convert an angle or a trigonometric ratios into the solvable format.
- Have the unit circle memorized to help you conserve time by knowing the exact values.
Compound Angle Formulas
Example 1
Double angle Formulas
Cosine
Sine
Subtraction Formulas
Addition Formulas
- Compound Angle: This can be obtained when finding the sum of two or more trigonometric angles. This can be found by adding and or subtracting the trigonometric angles.
- The compound angle formulas can be used to get the exact trigonometric values and to show that some trigonometric expressions are equivalent.
Example 2
Tangent
Example 1
sin(A + B) = sin A cos B + cos A sinB
cos(A + B) = cosA cosB - sinA sinB
tan(A + B) = tanA + tanB
1- tanAtanB
sin(A - B) = sin A cos B - cos A sinB
cos(A - B) = cosA cosB + sinA sinB
tan(A - B) = tanA - tanB
1+tanAtanB
Example 2
Review Questions
Things you need to know
Compound Angle:
- pg.401# 13
- pg.411# 6d,f
- pg.440#4a,b
Double Angle:
- pg.407#3d
- pg.411#10,11
- pg.440#6b,c
- To have an understanding to which where each formula can or cannot be used.
- To be able to recognize where the principle lies is the given intervals.
- To be able to use Pythagorean theorem in questions like example 2.
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