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Lesson: Directed Angles In Standard Position

Sample Question Videos

Worksheet • 19 Questions • 1 Video

Q1:

The terminal side of angle πœƒ in standard position intersects with the unit circle at the point, ( 2 π‘Ž , 3 π‘Ž ) where 0 < πœƒ < πœ‹ 2 . Find the value of π‘Ž .

  • A 1 √ 1 3
  • B √ 5
  • C 1 1 3
  • D 1 √ 5
  • E √ 1 3

Q2:

The terminal side of πœƒ intersects the unit circle at the point ( βˆ’ 2 0 π‘₯ , βˆ’ 5 π‘₯ ) where π‘₯ > 0 . Find the value πœƒ giving the answer to the nearest second.

  • A 1 9 4 2 β€² 1 0 β€² β€² ∘
  • B 1 6 5 5 7 β€² 5 0 β€² β€² ∘
  • C 3 4 5 5 7 β€² 5 0 β€² β€² ∘
  • D 1 4 2 β€² 1 0 β€² β€² ∘

Q3:

Is the angle in standard position?

  • Ano
  • Byes

Q4:

Is the angle in standard position?

  • Ayes
  • Bno

Q5:

Is the angle in standard position?

  • Ayes
  • Bno

Q6:

Is the angle in standard position?

  • Ayes
  • Bno

Q7:

Is the angle in standard position?

  • Ano
  • Byes

Q8:

Is the angle in standard position?

  • Ano
  • Byes

Q9:

Is the angle in standard position?

  • Ayes
  • Bno

Q10:

Find the value of c o t πœƒ where πœƒ is the measure of an angle in standard position whose terminal side passes through ( 0 , βˆ’ 6 ) .

Q11:

The terminal side of ∠ 𝐴 𝑂 𝐡 in standard position intersects the unit circle 𝑂 at the point 𝐡 with coordinates ο€Ώ 3 √ 1 0 , 𝑦  , where 𝑦 > 0 . Find the value of s i n 𝐴 𝑂 𝐡 .

  • A 1 √ 1 0
  • B 1 1 0
  • C 1 3
  • D 3 √ 1 0

Q12:

The terminal side of ∠ πœƒ intersects the unit circle at the point ο€Ό 8 1 7 , 𝑦  where 𝑦 > 0 . Find the value of ∠ πœƒ giving the answer to the nearest second and the value of 𝑦 as a fraction.

  • A π‘š ∠ πœƒ = 6 1 5 5 β€² 3 9 β€² β€² ∘ and 𝑦 = 1 5 1 7
  • B π‘š ∠ πœƒ = 2 4 1 5 5 β€² 3 9 β€² β€² ∘ and 𝑦 = 1 5 1 7
  • C π‘š ∠ πœƒ = 1 2 8 5 5 β€² 5 6 β€² β€² ∘ and 𝑦 = 8 1 5
  • D π‘š ∠ πœƒ = 6 1 5 5 β€² 3 9 β€² β€² ∘ and 𝑦 = βˆ’ 1 5 1 7

Q13:

Does the ordered pair express an angle in standard position?

  • Ayes
  • Bno

Q14:

The terminal side of πœƒ in standard position intersects with the unit circle at the point 𝐡 with coordinates ο€Ό βˆ’ 4 5 , βˆ’ 3 5  . Find the value of πœƒ giving the answer to the nearest second.

  • A 2 1 6 5 2 β€² 1 2 β€² β€² ∘
  • B 3 6 5 2 β€² 1 2 β€² β€² ∘
  • C 3 2 3 7 β€² 4 8 β€² β€² ∘
  • D 1 4 3 7 β€² 4 8 β€² β€² ∘

Q15:

Find the value of s e c πœƒ where πœƒ is the measure of an angle in standard position whose terminal side passes through ( 0 , βˆ’ 7 ) .

  • AUndefined
  • B0
  • C βˆ’ 1
  • D1

Q16:

In the given figure, point is on the unit circle and lies in the interval .

From the right triangle , what ratio gives ?

  • A
  • B
  • C
  • D
  • E

Which of the following is true concerning the triangles and ?

  • AThey are similar.
  • BThey are scalene.
  • CThey are congruent.
  • DThey are equilateral.
  • EThey are isosceles.

What is the scale factor of to ?

  • A
  • B
  • C
  • D
  • E

Use your answers to the previous parts to determine the length of in terms of and .

  • A
  • B
  • C
  • D
  • E

Q17:

Consider a windmill with blades of length 1 m. The position of the top 𝑃 of a given blade is given by its coordinates ( π‘Ž , 𝑏 ) which depend upon angle πœƒ as shown.

Express π‘Ž and 𝑏 as functions of the measure of angle πœƒ in radians.

  • A π‘Ž = πœƒ , 𝑏 = πœƒ c o s s i n
  • B π‘Ž = βˆ’ πœƒ , 𝑏 = βˆ’ πœƒ c o s s i n
  • C π‘Ž = πœƒ , 𝑏 = πœƒ s i n c o s
  • D π‘Ž = πœƒ , 𝑏 = πœƒ c o s t a n
  • E π‘Ž = πœƒ , 𝑏 = πœƒ t a n s i n

If the angle πœƒ at a certain time is 5 πœ‹ 3 , what will it be after the blade has completed half a rotation?

  • A 8 πœ‹ 3
  • B 4 πœ‹ 3
  • C 5 πœ‹ 3
  • D 3 πœ‹ 5
  • E 3 πœ‹ 8

Q18:

In the given figure, point is on the unit circle and lies in the interval .

Is positive or negative?

  • Apositive
  • Bnegative

Which of the following is true concerning the triangles , and ?

  • AThey are similar.
  • BThey are scalene.
  • CThey are congruent.
  • DThey are equilateral.
  • EThey are isosceles.

Q19:

Find the value of c s c πœƒ where πœƒ is the measure of an angle in standard position whose terminal side passes through ( βˆ’ 2 , 0 ) .

  • AUndefined
  • B0
  • C βˆ’ 1
  • D1
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