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−2524
  • B−257
  • C2524
  • D257

Q2:

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

  • A45
  • B−45
  • C34
  • D−34

Q3:

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

  • Asin𝜃=−1517, cos𝜃=817, tan𝜃=158, csc𝜃=1715, sec𝜃=178
  • Bsin𝜃=1517, cos𝜃=817, tan𝜃=−158, csc𝜃=−1715, sec𝜃=−178
  • Csin𝜃=−1517, cos𝜃=817, tan𝜃=−158, csc𝜃=−1715, sec𝜃=178
  • Dsin𝜃=−1517, cos𝜃=−817, tan𝜃=158, csc𝜃=−1715, sec𝜃=178

Q4:

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

  • A139
  • B913
  • C−913
  • D−139
  • E−52

Q5:

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

  • A√137
  • B−67
  • C−√136
  • D67
  • E−√137

Q6:

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

Hint: Take cscsincos(2𝜃)=12(𝜃)(𝜃).

  • A9√24
  • B−9√28
  • C9√28
  • D2√29
  • E−4√29

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√15+2√212
  • B√15−2√212
  • C√26
  • D−√15−2√212
  • E−√15+2√212

Q8:

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

Hint: Take tantantantantan(𝜃+𝜃)=(𝜃)+(𝜃)1−(𝜃)(𝜃).

  • A9√24
  • B7√28
  • C−7√28
  • D−4√27
  • E4√27

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