Worksheet: Reciprocal and Quotient Identities

In this worksheet, we will practice finding trigonometric functions such as tangent, cotangent, secant, and cosecant, in terms of sine and cosine.

Q1:

Which of the following is equal to tan69?

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

Q2:

Find the value of 2𝜃𝜃+11𝜃𝜃+7𝜃𝜃sincsccossectancot.

Q3:

Which of the following is equivalent to sincos𝜃𝜃?

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

Q4:

Find the value of tan𝜃 given 11𝜃13𝜃11𝜃+13𝜃=23cossincossin.

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

Q5:

Which of the following expressions is equivalent to csc𝜃?

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

Q6:

Which of the following expressions is equivalent to sec𝜃?

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

Q7:

Which of the following expressions is equivalent to 1𝜃csc?

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

Q8:

Which of the following expressions is equivalent to 1𝜃cot?

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

Q9:

Which of the following expressions is equivalent to 1𝜃tan?

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

Q10:

Which of the following expressions is equivalent to cot𝜃?

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

Q11:

Which of the following expressions is equivalent to tan𝜃?

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

Q12:

Which of the following expressions is equivalent to 1𝜃sec?

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

Q13:

Complete the following: cos𝜃=1.

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

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