Lesson Worksheet: Evaluating Trigonometric Ratios given the Value of Another Ratio Mathematics

Start Practising

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

Q1:

True of False: If sin𝜃=35 and cos𝜃<0, then tan𝜃=−34.

  • AFalse
  • BTrue

Q2:

Find sin𝐵 given tan𝐵=43 and cos𝐵=35.

  • A1225
  • B245
  • C45
  • D140

Q3:

Find tan𝐴 given sin𝐴=0.5 and cos𝐴=√32.

  • A√3
  • B1√3
  • C503
  • D350

Q4:

If cot(𝜃)=−43 and cos(𝜃)>0, find csc(𝜃).

  • A53
  • B54
  • C−35
  • D−53
  • E−54

Q5:

Find cot𝜃 given sin𝜃=35 where 90<𝜃<180∘∘.

  • A43
  • B−34
  • C−43
  • D34

Q6:

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

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

Q7:

Evaluate the other five trigonometric functions given that sin(𝜃)=35 and 0<𝜃<𝜋2.

  • Acos(𝜃)=45, tan(𝜃)=43, sec(𝜃)=54, csc(𝜃)=53, and cot(𝜃)=34
  • Bcos(𝜃)=45, tan(𝜃)=34, sec(𝜃)=53, csc(𝜃)=54, and cot(𝜃)=43
  • Ccos(𝜃)=54, tan(𝜃)=34, sec(𝜃)=45, csc(𝜃)=53, and cot(𝜃)=43
  • Dcos(𝜃)=45, tan(𝜃)=34, sec(𝜃)=54, csc(𝜃)=53, and cot(𝜃)=43
  • Ecos(𝜃)=43, tan(𝜃)=53, sec(𝜃)=54, csc(𝜃)=34, and cot(𝜃)=45

Q8:

Find the value of seccsccot(𝜃)(𝜃)−(𝜃), given that 180<𝜃<270∘∘ and sin(𝜃)=−35.

  • A−4112
  • B34
  • C4112
  • D−27100
  • E123100

Q9:

Find the value of cotcsctansec𝜃−𝜃𝜃−𝜃 given 𝜃∈3𝜋2,2𝜋 and sin𝜃=−45.

  • A−16
  • B−1131
  • C16
  • D1131

Q10:

Find the value of sincoscossin𝛼𝛽−𝛼𝛽, given tan𝛼=34 where 𝛼 is the smallest positive angle and tan𝛽=158 where 180<𝛽<270∘∘.

  • A−1385
  • B1385
  • C3685
  • D−3685

This lesson includes 28 additional questions and 308 additional question variations for subscribers.

GET YOUR PORTAL NOW

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.