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Worksheet: Equivalent Forms of Trigonometric Identities

Q1:

Which of the following expressions is equivalent to c o s s i n 1 2 π‘₯ + 6 π‘₯ 2 ?

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

Q2:

Which of the following expressions is equivalent to c o s s i n 2 2 πœ‹ 4 βˆ’ πœ‹ 4 ?

  • A s i n πœ‹ 2
  • B c o s πœ‹ 4
  • C 2 πœ‹ 4 s i n
  • D c o s πœ‹ 2
  • E 2 πœ‹ 4 c o s

Q3:

Which of the following three identities are true?

  • A c o s c o s s i n s i n t a n t a n ( βˆ’ πœƒ ) = πœƒ , ( βˆ’ πœƒ ) = πœƒ , ( βˆ’ πœƒ ) = πœƒ
  • B c o s c o s s i n s i n t a n t a n ( βˆ’ πœƒ ) = βˆ’ πœƒ , ( βˆ’ πœƒ ) = βˆ’ πœƒ , ( βˆ’ πœƒ ) = πœƒ
  • C c o s c o s s i n s i n t a n t a n ( βˆ’ πœƒ ) = βˆ’ πœƒ , ( βˆ’ πœƒ ) = πœƒ , ( βˆ’ πœƒ ) = βˆ’ πœƒ
  • D c o s c o s s i n s i n t a n t a n ( βˆ’ πœƒ ) = πœƒ , ( βˆ’ πœƒ ) = βˆ’ πœƒ , ( βˆ’ πœƒ ) = βˆ’ πœƒ
  • E c o s c o s s i n s i n t a n t a n ( βˆ’ πœƒ ) = βˆ’ πœƒ , ( βˆ’ πœƒ ) = βˆ’ πœƒ , ( βˆ’ πœƒ ) = βˆ’ πœƒ

Q4:

Which of the following is equivalent to 1 βˆ’ 2 πœƒ s i n 2 ∘ ?

  • A 2 2 πœƒ c o s ∘
  • B βˆ’ 2 πœƒ s i n ∘
  • C s i n πœƒ ∘
  • D c o s 2 πœƒ ∘
  • E βˆ’ 2 πœƒ c o s ∘

Q5:

Which of the following is not a trigonometric identity?

  • A c o s πœƒ = 1 2
  • B s i n s i n ( βˆ’ πœƒ ) = βˆ’ πœƒ

Q6:

Which of the following expressions is equal to s i n c o s c o s s i n ο€» πœ‹ 2 βˆ’ πœƒ  πœƒ βˆ’ ο€» πœ‹ 2 βˆ’ πœƒ  ( πœ‹ βˆ’ πœƒ ) ?

  • A 2 πœƒ s i n 2
  • B 2 πœƒ c o s 2
  • C 2 2 πœƒ s i n
  • D c o s s i n 2 2 πœƒ βˆ’ πœƒ
  • E 2 πœƒ πœƒ s i n c o s

Q7:

Which of the following is a trigonometric identity?

  • A 1 + πœƒ = πœƒ t a n s e c 2 2
  • B c o s πœƒ = √ 3 2

Q8:

Which of the following is a trigonometric identity?

  • A s i n c s c πœƒ = 1 πœƒ
  • B s i n πœƒ = 1 2