Lesson Worksheet: Evaluating Trigonometric Ratios given the Value of Another Ratio Mathematics • 10th Grade

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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:

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:

Given that sin(𝜃)=35 and 0<𝜃<𝜋2, evaluate cos(𝜃), tan(𝜃), sec(𝜃), csc(𝜃), and cot(𝜃).

  • 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

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