Worksheet: Evaluating Trigonometric Functions

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In this worksheet, we will practice finding the value of a trigonometric function from a given value of another trigonometric function.

Q1:

Find csc𝜃 given tan𝜃=247 and cos𝜃<0.

  • A − 2 5 2 4
  • B − 2 5 7
  • C 2 5 2 4
  • D 2 5 7

Q2:

Find the value of cos(180−𝜃)∘ given sin𝜃=−35 where 270<𝜃<360∘∘.

  • A 4 5
  • B − 4 5
  • C 3 4
  • D − 3 4

Q3:

Find all the trigonometric ratios of 𝜃 given cot𝜃=−815 where 𝜃∈3𝜋2,2𝜋.

  • A s i n 𝜃 = − 1 5 1 7 , c o s 𝜃 = 8 1 7 , t a n 𝜃 = 1 5 8 , c s c 𝜃 = 1 7 1 5 , s e c 𝜃 = 1 7 8
  • B s i n 𝜃 = 1 5 1 7 , c o s 𝜃 = 8 1 7 , t a n 𝜃 = − 1 5 8 , c s c 𝜃 = − 1 7 1 5 , s e c 𝜃 = − 1 7 8
  • C s i n 𝜃 = − 1 5 1 7 , c o s 𝜃 = 8 1 7 , t a n 𝜃 = − 1 5 8 , c s c 𝜃 = − 1 7 1 5 , s e c 𝜃 = 1 7 8
  • D s i n 𝜃 = − 1 5 1 7 , c o s 𝜃 = − 8 1 7 , t a n 𝜃 = 1 5 8 , c s c 𝜃 = − 1 7 1 5 , s e c 𝜃 = 1 7 8

Q4:

Given that cot(𝜃)=−32, where 𝜋2<𝜃<𝜋, evaluate sec(𝜃) without using a calculator.

  • A 1 3 9
  • B 9 1 3
  • C − 9 1 3
  • D − 1 3 9
  • E − 5 2

Q5:

Given that csc𝜃=−76 and tan𝜃>0, find cos𝜃.

  • A √ 1 3 7
  • B − 6 7
  • C − √ 1 3 6
  • D 6 7
  • E − √ 1 3 7

Q6:

Given that sin(𝜃)=−13, where 𝜋<𝜃<3𝜋2, evaluate csc(2𝜃) without using a calculator.

Hint: Take cscsincos(2𝜃)=12(𝜃)(𝜃).

  • A 9 √ 2 4
  • B − 9 √ 2 8
  • C 9 √ 2 8
  • D 2 √ 2 9
  • E − 4 √ 2 9

Q7:

Given that sin(𝜃)=13, where 0<𝜃<𝜋2, and cos(𝜃)=14, where 0<𝜃<𝜋2, evaluate cos(𝜃+𝜃) without using a calculator.

Hint: Take coscoscossinsin(𝜃+𝜃)=(𝜃)(𝜃)−(𝜃)(𝜃).

  • A √ 1 5 + 2 √ 2 1 2
  • B √ 1 5 − 2 √ 2 1 2
  • C √ 2 6
  • D − √ 1 5 − 2 √ 2 1 2
  • E − √ 1 5 + 2 √ 2 1 2

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