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

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


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

  • AFalse
  • BTrue


Find sin𝐵 given tan𝐵=43 and cos𝐵=35.

  • A1225
  • B245
  • C45
  • D140


Find tan𝐴 given sin𝐴=0.5 and cos𝐴=32.

  • A3
  • B13
  • C503
  • D350


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

  • A53
  • B54
  • C35
  • D53
  • E54


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

  • A43
  • B34
  • C43
  • D34


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

  • A139
  • B913
  • C913
  • D139
  • E52


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


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

  • A4112
  • B34
  • C4112
  • D27100
  • E123100


Find the value of cotcsctansec𝜃𝜃𝜃𝜃 given 𝜃3𝜋2,2𝜋 and sin𝜃=45.

  • A16
  • B1131
  • C16
  • D1131


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

  • A1385
  • B1385
  • C3685
  • D3685

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

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