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Lesson: Trigonometric Ratios and the Unit Circle

Sample Question Videos

Worksheet • 14 Questions • 2 Videos

Q1:

In the figure, points 𝑀 ( πœƒ , πœƒ ) c o s s i n and 𝑁 lie on the unit circle, and ∠ 𝐴 𝑂 𝑁 = 2 πœ‹ βˆ’ πœƒ .

Express the values of sine, cosine, and tangent of 2 πœ‹ βˆ’ πœƒ in terms of their values for πœƒ . Check whether this is valid for all values of πœƒ .

  • A c o s c o s s i n s i n t a n t a n ( 2 πœ‹ βˆ’ πœƒ ) = πœƒ , ( 2 πœ‹ βˆ’ πœƒ ) = βˆ’ πœƒ , ( 2 πœ‹ βˆ’ πœƒ ) = βˆ’ πœƒ
  • B c o s c o s s i n s i n t a n t a n ( 2 πœ‹ βˆ’ πœƒ ) = βˆ’ πœƒ , ( 2 πœ‹ βˆ’ πœƒ ) = πœƒ , ( 2 πœ‹ βˆ’ πœƒ ) = πœƒ
  • C c o s c o s s i n s i n t a n t a n ( 2 πœ‹ βˆ’ πœƒ ) = βˆ’ πœƒ , ( 2 πœ‹ βˆ’ πœƒ ) = βˆ’ πœƒ , ( 2 πœ‹ βˆ’ πœƒ ) = βˆ’ πœƒ
  • D c o s c o s s i n s i n t a n t a n ( 2 πœ‹ βˆ’ πœƒ ) = πœƒ , ( 2 πœ‹ βˆ’ πœƒ ) = βˆ’ πœƒ , ( 2 πœ‹ βˆ’ πœƒ ) = πœƒ
  • E c o s c o s s i n s i n t a n t a n ( 2 πœ‹ βˆ’ πœƒ ) = πœƒ , ( 2 πœ‹ βˆ’ πœƒ ) = πœƒ , ( 2 πœ‹ βˆ’ πœƒ ) = βˆ’ πœƒ

Q2:

Find s e c πœƒ , given πœƒ is in standard position and its terminal side passes through the point ο€Ό 4 5 , 3 5  .

  • A 5 4
  • B 3 5
  • C 5 3
  • D 4 5

Q3:

Find s i n πœƒ , given πœƒ is in standard position and its terminal side passes through the point ο€Ό 3 5 , βˆ’ 4 5  .

  • A βˆ’ 4 5
  • B 4 5
  • C 3 5
  • D βˆ’ 3 5
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