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Worksheet: Reciprocal and Quotient Identities

Q1:

Which of the following is equal to t a n 6 9 ?

  • A 3 2 3 t a n
  • B c o s s i n 6 9 6 9
  • C 3 2 3 2 3 s i n c o s
  • D s i n c o s 6 9 6 9

Q2:

Which of the following is equal to t a n 2 2 ?

  • A 2 1 1 t a n
  • B c o s s i n 2 2 2 2
  • C 2 1 1 1 1 s i n c o s
  • D s i n c o s 2 2 2 2

Q3:

Which of the following is equal to t a n 5 1 ?

  • A 3 1 7 t a n
  • B c o s s i n 5 1 5 1
  • C 3 1 7 1 7 s i n c o s
  • D s i n c o s 5 1 5 1

Q4:

Which of the following expressions is equivalent to c o t 𝜃 ?

  • A 1 𝜃 c o s
  • B s i n c o s 𝜃 𝜃
  • C 1 𝜃 s i n
  • D c o s s i n 𝜃 𝜃
  • E 1 𝜃 s e c

Q5:

Find the value of 2 𝜃 𝜃 + 1 1 𝜃 𝜃 + 7 𝜃 𝜃 s i n c s c c o s s e c t a n c o t .

Q6:

Find s i n 𝐵 given t a n 𝐵 = 4 3 and c o s 𝐵 = 3 5 .

  • A 1 4 0
  • B 1 2 2 5
  • C 2 4 5
  • D 4 5

Q7:

Find the value of t a n 𝜃 given 1 1 𝜃 1 3 𝜃 1 1 𝜃 + 1 3 𝜃 = 2 3 c o s s i n c o s s i n .

  • A 1 1 1 3
  • B 1 1 1 3
  • C 5 5 1 3
  • D 1 1 6 5

Q8:

Which of the following expressions is equivalent to c s c 𝜃 ?

  • A 1 𝜃 s e c
  • B 1 𝜃 c o s
  • C 1 𝜃 c o t
  • D 1 𝜃 s i n
  • E 1 𝜃 c s c

Q9:

Which of the following expressions is equivalent to s e c 𝜃 ?

  • A 1 𝜃 s e c
  • B 1 𝜃 s i n
  • C 1 𝜃 c o t
  • D 1 𝜃 c o s
  • E 1 𝜃 c o s e c

Q10:

Which of the following expressions is equivalent to 1 𝜃 c o s e c ?

  • A t a n 𝜃
  • B c o s 𝜃
  • C c o t 𝜃
  • D s i n 𝜃
  • E s e c 𝜃

Q11:

Which of the following expressions is equivalent to 1 𝜃 c o t ?

  • A c o s 𝜃
  • B s i n 𝜃
  • C s e c 𝜃
  • D t a n 𝜃
  • E c o s e c 𝜃

Q12:

Which of the following expressions is equivalent to 1 𝜃 t a n ?

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