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?

  • A32323sincos
  • Bsincos6969
  • C323tan
  • Dcossin6969

Q2:

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

Q3:

Which of the following is equivalent to sincos𝜃𝜃?

  • Acsc𝜃
  • Btan𝜃
  • Ccot𝜃
  • Dsec𝜃

Q4:

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

  • A1113
  • B1113
  • C1165
  • D5513

Q5:

Which of the following expressions is equivalent to csc𝜃?

  • A1𝜃csc
  • B1𝜃sin
  • C1𝜃cot
  • D1𝜃sec
  • E1𝜃cos

Q6:

Which of the following expressions is equivalent to sec𝜃?

  • A1𝜃sin
  • B1𝜃cot
  • C1𝜃sec
  • D1𝜃cosec
  • E1𝜃cos

Q7:

Which of the following expressions is equivalent to 1𝜃csc?

  • Atan𝜃
  • Bcos𝜃
  • Csec𝜃
  • Dsin𝜃
  • Ecot𝜃

Q8:

Which of the following expressions is equivalent to 1𝜃cot?

  • Acosec𝜃
  • Btan𝜃
  • Ccos𝜃
  • Dsec𝜃
  • Esin𝜃

Q9:

Which of the following expressions is equivalent to 1𝜃tan?

  • Asec𝜃
  • Bcsc𝜃
  • Ccos𝜃
  • Dsin𝜃
  • Ecot𝜃

Q10:

Which of the following expressions is equivalent to cot𝜃?

  • Asincos𝜃𝜃
  • B1𝜃sin
  • C1𝜃cos
  • D1𝜃sec
  • Ecossin𝜃𝜃

Q11:

Which of the following expressions is equivalent to tan𝜃?

  • A1𝜃sin
  • Bcossin𝜃𝜃
  • C1𝜃cos
  • D1𝜃sec
  • Esincos𝜃𝜃

Q12:

Which of the following expressions is equivalent to 1𝜃sec?

  • Asin𝜃
  • Bcos𝜃
  • Ccosec𝜃
  • Dtan𝜃
  • Ecot𝜃

Q13:

Complete the following: cos𝜃=1.

  • Asin𝜃
  • Bcot𝜃
  • Csec𝜃
  • Dcsc𝜃

Q14:

Find cot𝐵 given that 𝐴𝐵𝐶 is a right triangle at 𝐶, where 𝐴𝐶=12cm and 𝐵𝐶=9cm.

  • A53
  • B35
  • C34
  • D43
  • E45

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