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Cogito

Integrated Math 3 · Chapter 6 · Lesson 2

Practice Worksheet

Sum, Difference, and Double Angle

Sine does not distribute.

12 problems · about 22 minutes · F-TF.C.9

NameDate

Figure — use these to answer the problems

Set the angle to 45°, then to 30°, then to 75°. The third value comes from combining the first two.
(0.259, 0.966)
  • Angle75° = 5π/12 rad
  • x-coordinate0.259
  • y-coordinate0.966
  • cos 75°0.259
  • sin 75°0.966
Angle in degrees75
Figure 1

Warm Up

Straightforward practice. Get the method working first.

5 problems

  1. sin A = 0.6 and cos A = 0.8. What is cos 2A?

    Answer

  2. Which formula reverses the sign between its products?

    • The cosine sum and difference formulas.
    • The sine formulas.

  3. sin A = 0.6, cos A = 0.8. What is sin 2A?

    Answer

  4. Same values. What is cos 2A?

    Answer

  5. sin A = 0.5, cos A = 0.866. What is sin 2A, to three decimal places?

    Answer

Build It Up

The same ideas with more to keep track of.

3 problems

  1. 75° is the sum of 45° and which angle, in degrees?

    Answer

  2. In cos(A + B), what sign sits between the two products? 1 plus, 2 minus.

    Answer

  3. How many equivalent forms does cos 2A have?

    Answer

Stretch Yourself

Mixed problems. Work out what kind of question it is before you start.

4 problems

  1. Sort each formula by which sign it uses between the products.

    Write each item under the heading it belongs to: sin(A plus B) · sin(A minus B) · cos(A plus B) · cos(A minus B)

    Keeps the operation sign

    Reverses the sign

  2. sin A = 0.8, cos A = 0.6. What is sin 2A?

    Answer

  3. The Test

    Is sin(A + B) equal to sin A + sin B? 1 yes, 0 no.

    Answer

  4. The Double

    sin A = 0.6 and cos A = 0.8. What is sin 2A?

    Answer