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Worksheet: Trigonometric Ratios on the Unit Circle

Q1:

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

Q2:

Find t a n πœƒ given πœƒ is in standard position and its terminal side passes through the point ο€Ό βˆ’ 3 5 , βˆ’ 4 5  .

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

Q3:

Is c o s 4 0 0 ∘ positive or negative?

  • Apositive
  • Bnegative

Q4:

Is t a n 6 5 ∘ positive or negative?

  • Apositive
  • Bnegative

Q5:

Is c o s 6 6 0 ∘ positive or negative?

  • Apositive
  • Bnegative

Q6:

Is s i n 6 0 5 ∘ positive or negative?

  • Anegative
  • Bpositive

Q7:

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 4 5
  • B 3 5
  • C 5 3
  • D 5 4

Q8:

If the angle πœƒ is in the standard position, c o s πœƒ = βˆ’ √ 2 2 and s i n πœƒ = βˆ’ √ 2 2 , is it possible for πœƒ to measure 135?

  • Ano
  • Byes

Q9:

In which quadrant does πœƒ lie if s i n πœƒ = 1 √ 2 and c o s πœƒ = 1 √ 2 ?

  • A the third
  • B the second
  • C the fourth
  • D the first

Q10:

In which quadrant does πœƒ lie if s i n πœƒ > 0 and c o s πœƒ > 0 ?

  • Athird
  • Bsecond
  • Cfourth
  • Dfirst

Q11:

In which quadrant does πœƒ lie if s i n πœƒ > 0 and t a n πœƒ > 0 ?

  • Athird
  • Bsecond
  • Cfourth
  • Dfirst

Q12:

In which quadrant does πœƒ lie if s i n πœƒ > 0 and c o s πœƒ < 0 ?

  • Athird
  • Bfirst
  • Cfourth
  • Dsecond

Q13:

In which quadrant does πœƒ lie if c o s πœƒ > 0 and t a n πœƒ < 0 ?

  • Asecond
  • Bfirst
  • Cthird
  • Dfourth

Q14:

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 ) = 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 ) = βˆ’ πœƒ , ( 2 πœ‹ βˆ’ πœƒ ) = βˆ’ 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 ) = πœƒ , ( 2 πœ‹ βˆ’ πœƒ ) = βˆ’ πœƒ , ( 2 πœ‹ βˆ’ πœƒ ) = 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 ) = βˆ’ 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 ) = βˆ’ πœƒ , ( 2 πœ‹ βˆ’ πœƒ ) = πœƒ , ( 2 πœ‹ βˆ’ πœƒ ) = πœƒ