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Lesson: Integrating Products of Sines and Cosines

In this lesson, we will learn how to evaluate integrals of products of sines and cosines with different arguments using trigonometric product-to-sum identities.

Worksheet • 5 Questions

Q1:

Determine ο„Έ ( βˆ’ 8 4 π‘₯ 9 π‘₯ ) π‘₯ s i n s i n d .

  • A βˆ’ 4 5 5 π‘₯ + 4 1 3 1 3 π‘₯ + s i n s i n C
  • B βˆ’ 2 0 5 π‘₯ + 5 2 1 3 π‘₯ + s i n s i n C
  • C 4 5 5 π‘₯ βˆ’ 4 1 3 1 3 π‘₯ + s i n s i n C
  • D 4 5 π‘₯ βˆ’ 4 1 3 π‘₯ + s i n s i n C
  • E βˆ’ 4 5 π‘₯ + 4 1 3 π‘₯ + s i n s i n C

Q2:

Determine ο„Έ ( βˆ’ 6 4 π‘₯ 7 π‘₯ ) π‘₯ s i n s i n d .

  • A βˆ’ 3 π‘₯ + 3 1 1 1 1 π‘₯ + s i n s i n C
  • B βˆ’ 9 3 π‘₯ + 3 3 1 1 π‘₯ + s i n s i n C
  • C s i n s i n C 3 π‘₯ βˆ’ 3 1 1 1 1 π‘₯ +
  • D βˆ’ 3 3 π‘₯ βˆ’ 3 1 1 π‘₯ + s i n s i n C
  • E 3 3 π‘₯ + 3 1 1 π‘₯ + s i n s i n C

Q3:

Determine ο„Έ ( 5 5 π‘₯ 8 π‘₯ ) π‘₯ s i n s i n d .

  • A 5 6 3 π‘₯ βˆ’ 5 2 6 1 3 π‘₯ + s i n s i n C
  • B 1 5 2 3 π‘₯ βˆ’ 6 5 2 1 3 π‘₯ + s i n s i n C
  • C βˆ’ 5 6 3 π‘₯ + 5 2 6 1 3 π‘₯ + s i n s i n C
  • D 5 2 3 π‘₯ + 5 2 1 3 π‘₯ + s i n s i n C
  • E βˆ’ 5 2 3 π‘₯ βˆ’ 5 2 1 3 π‘₯ + s i n s i n C

Q4:

Determine ο„Έ ( βˆ’ 2 2 π‘₯ 7 π‘₯ ) π‘₯ s i n s i n d .

  • A βˆ’ 1 5 5 π‘₯ + 1 9 9 π‘₯ + s i n s i n C
  • B βˆ’ 5 5 π‘₯ + 9 9 π‘₯ + s i n s i n C
  • C 1 5 5 π‘₯ βˆ’ 1 9 9 π‘₯ + s i n s i n C
  • D βˆ’ 5 π‘₯ βˆ’ 9 π‘₯ + s i n s i n C
  • E s i n s i n C 5 π‘₯ + 9 π‘₯ +

Q5:

Determine ο„Έ ( 2 4 π‘₯ 7 π‘₯ ) π‘₯ s i n s i n d .

  • A 1 3 3 π‘₯ βˆ’ 1 1 1 1 1 π‘₯ + s i n s i n C
  • B 3 3 π‘₯ βˆ’ 1 1 1 1 π‘₯ + s i n s i n C
  • C βˆ’ 1 3 3 π‘₯ + 1 1 1 1 1 π‘₯ + s i n s i n C
  • D s i n s i n C 3 π‘₯ + 1 1 π‘₯ +
  • E βˆ’ 3 π‘₯ βˆ’ 1 1 π‘₯ + s i n s i n C
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