Worksheet: Equivalent Forms of Trigonometric Identities

In this worksheet, we will practice using trigonometric identities to rewrite expressions in equivalent forms and using that to solve problems.

Q1:

Is t a n s i n c o s 𝜃 = 𝜃 𝜃 an identity or an equation?

  • Aan identity
  • Ban equation

Q2:

Which of the following is a trigonometric identity?

  • A 1 + 𝜃 = 𝜃 t a n s e c 2 2
  • B c o s 𝜃 = 3 2

Q3:

Which of the following expressions is equivalent to c o s s i n 1 2 𝑥 + 6 𝑥 2 ?

  • A c o s s i n 2 2 6 𝑥 6 𝑥
  • B 2 6 𝑥 c o s 2
  • C 2 6 𝑥 + 1 6 𝑥 c o s s i n 2 2
  • D 1 6 𝑥 s i n 2
  • E 2 6 𝑥 6 𝑥 s i n c o s

Q4:

Which of the following expressions is equivalent to c o s s i n 2 2 𝜋 4 𝜋 4 ?

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

Q5:

Which of the following expressions is equal to s i n c o s c o s s i n 𝜋 2 𝜃 𝜃 𝜋 2 𝜃 ( 𝜋 𝜃 ) ?

  • A 2 𝜃 s i n 2
  • B 2 𝜃 c o s 2
  • C 2 2 𝜃 s i n
  • D c o s s i n 2 2 𝜃 𝜃
  • E 2 𝜃 𝜃 s i n c o s

Q6:

Which of the following is not a trigonometric identity?

  • A c o s 𝜃 = 1 2
  • B s i n s i n ( 𝜃 ) = 𝜃

Q7:

Which of the following is equivalent to 1 2 𝜃 s i n 2 ?

  • A 2 2 𝜃 c o s
  • B 2 𝜃 s i n
  • C s i n 𝜃
  • D c o s 2 𝜃
  • E 2 𝜃 c o s

Q8:

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 ( 𝜃 ) = 𝜃 , ( 𝜃 ) = 𝜃 , ( 𝜃 ) = 𝜃
  • B c o s c o s s i n s i n t a n t a n ( 𝜃 ) = 𝜃 , ( 𝜃 ) = 𝜃 , ( 𝜃 ) = 𝜃
  • C c o s c o s s i n s i n t a n t a n ( 𝜃 ) = 𝜃 , ( 𝜃 ) = 𝜃 , ( 𝜃 ) = 𝜃
  • D c o s c o s s i n s i n t a n t a n ( 𝜃 ) = 𝜃 , ( 𝜃 ) = 𝜃 , ( 𝜃 ) = 𝜃
  • E c o s c o s s i n s i n t a n t a n ( 𝜃 ) = 𝜃 , ( 𝜃 ) = 𝜃 , ( 𝜃 ) = 𝜃

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