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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.

  • Lots of Practice!

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.

  • Lots of Practice !!

MATH JOURNEY

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