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

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 sinπœƒ=35 and cosπœƒ<0, then tanπœƒ=βˆ’34.

  • AFalse
  • BTrue


Find sin𝐡 given tan𝐡=43 and cos𝐡=35.

  • A1225
  • B245
  • C45
  • D140


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

  • A√3
  • B1√3
  • C503
  • D350


If cot(πœƒ)=βˆ’43 and cos(πœƒ)>0, find csc(πœƒ).

  • A53
  • B54
  • Cβˆ’35
  • Dβˆ’53
  • Eβˆ’54


Find cotπœƒ given sinπœƒ=35 where 90<πœƒ<180∘∘.

  • A43
  • Bβˆ’34
  • Cβˆ’43
  • D34


Given that cot(πœƒ)=βˆ’32, where πœ‹2<πœƒ<πœ‹, evaluate sec(πœƒ) without using a calculator.

  • A139
  • B913
  • Cβˆ’913
  • Dβˆ’139
  • Eβˆ’52


Given that sin(πœƒ)=35 and 0<πœƒ<πœ‹2, evaluate cos(πœƒ), tan(πœƒ), sec(πœƒ), csc(πœƒ), and cot(πœƒ).

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


Find the value of seccsccot(πœƒ)(πœƒ)βˆ’(πœƒ), given that 180<πœƒ<270∘∘ and sin(πœƒ)=βˆ’35.

  • Aβˆ’4112
  • B34
  • C4112
  • Dβˆ’27100
  • E123100


Find the value of cotcsctansecπœƒβˆ’πœƒπœƒβˆ’πœƒ given πœƒβˆˆο€Ό3πœ‹2,2πœ‹οˆ and sinπœƒ=βˆ’45.

  • Aβˆ’16
  • Bβˆ’1131
  • C16
  • D1131


Find the value of sincoscossinπ›Όπ›½βˆ’π›Όπ›½, given tan𝛼=34 where 𝛼 is the smallest positive angle and tan𝛽=158 where 180<𝛽<270∘∘.

  • Aβˆ’1385
  • B1385
  • C3685
  • Dβˆ’3685

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