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Lesson: Solving Equations Using Cofunction Identities

Worksheet • 25 Questions

Q1:

Simplify s i n ( πœƒ βˆ’ 2 7 0 ) ∘ .

  • A c o s πœƒ
  • B s i n πœƒ
  • C βˆ’ πœƒ s i n
  • D βˆ’ πœƒ c o s

Q2:

Simplify s e c t a n t a n πœƒ πœƒ ( 2 7 0 + πœƒ ) ∘ .

  • A βˆ’ πœƒ s e c
  • B c s c πœƒ
  • C βˆ’ πœƒ s i n 2
  • D s e c πœƒ

Q3:

Which of the following is the general solution of the equation c s c s e c 6 πœƒ = 3 πœƒ ?

  • A πœ‹ 1 8 + 2 πœ‹ 𝑛 9 or πœ‹ 6 + 2 πœ‹ 𝑛 3 , where 𝑛 ∈ β„€
  • B 2 πœ‹ 9 + 2 πœ‹ 𝑛 9 or 2 πœ‹ 3 + 2 πœ‹ 𝑛 3 , where 𝑛 ∈ β„€
  • C πœ‹ 1 8 βˆ’ 2 πœ‹ 𝑛 9 or πœ‹ 6 + 2 πœ‹ 𝑛 3 , where 𝑛 ∈ β„€
  • D πœ‹ 9 + πœ‹ 𝑛 9 or πœ‹ 3 βˆ’ πœ‹ 𝑛 3 , where 𝑛 ∈ β„€

Q4:

𝐴 𝐡 𝐢 𝐷 is a trapezium where π‘š ∠ 𝐴 = π‘š ∠ 𝐷 = 9 0 ∘ , 𝐢 𝐷 = 2 1 c m , 𝐴 𝐷 = 1 2 c m , and 𝐴 𝐡 = 3 0 c m . Find s i n πœƒ .

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

Q5:

𝐴 𝐡 𝐢 𝐷 is a square where 9 𝐷 𝐹 = 1 0 𝐹 𝐢 . Find the exact value of c o s πœƒ .

  • A 9 √ 4 4 2
  • B √ 4 4 2 1 9
  • C 1 9 √ 4 4 2
  • D √ 4 4 2 9

Q6:

Simplify s i n ( 2 7 0 βˆ’ πœƒ ) ∘ .

  • A βˆ’ πœƒ c o s
  • B βˆ’ πœƒ s i n
  • C s i n πœƒ
  • D c o s πœƒ

Q7:

Find the value of s e c c s c 1 0 5 1 5 ∘ ∘ .

Q8:

Find the value of π‘₯ given t a n c o t 7 8 = π‘₯ ∘ .

Q9:

Find the value of π‘₯ given c s c s e c 2 7 = π‘₯ ∘ .

Q10:

Find the value of π‘₯ given c s c s e c 8 0 = π‘₯ ∘ .

Q11:

Simplify s i n ( 9 0 + πœƒ ) ∘ .

  • A c o s πœƒ
  • B s i n πœƒ
  • C c s c πœƒ
  • D s e c πœƒ

Q12:

Simplify c o t ( 9 0 βˆ’ πœƒ ) ∘ .

  • A t a n πœƒ
  • B s e c πœƒ
  • C c o t πœƒ
  • D c s c πœƒ

Q13:

Find πœƒ in degrees given c o s s i n 1 5 3 1 5 β€² = βˆ’ πœƒ ∘ where πœƒ is an acute angle.

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

Q14:

Find πœƒ in degrees given s e c c s c 1 6 4 = βˆ’ πœƒ ∘ where πœƒ is an acute angle.

  • A 7 4 ∘
  • B 1 6 ∘
  • C 1 0 6 ∘
  • D 1 9 6 ∘

Q15:

Find πœƒ in degrees given s i n c o s 1 4 2 = πœƒ ∘ where πœƒ is an acute angle.

  • A 5 2 ∘
  • B 3 8 ∘
  • C 1 2 8 ∘
  • D 2 1 8 ∘

Q16:

Simplify c o t ( 2 7 0 βˆ’ πœƒ ) ∘ .

  • A t a n πœƒ
  • B βˆ’ πœƒ c o t
  • C c o t πœƒ
  • D βˆ’ πœƒ t a n

Q17:

Find πœƒ in degrees given c s c c s c 3 2 7 4 5 β€² = βˆ’ πœƒ ∘ where πœƒ is an acute angle.

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

Q18:

Simplify s e c ( 2 7 0 βˆ’ πœƒ ) ∘ .

  • A βˆ’ πœƒ c s c
  • B s e c πœƒ
  • C βˆ’ πœƒ s e c
  • D c s c πœƒ

Q19:

Simplify c s c ( 9 0 βˆ’ πœƒ ) ∘ .

  • A s e c πœƒ
  • B s i n πœƒ
  • C c s c πœƒ
  • D c o s πœƒ

Q20:

Simplify s e c ( 9 0 βˆ’ πœƒ ) ∘ .

  • A c s c πœƒ
  • B s e c πœƒ
  • C c o s πœƒ
  • D s i n πœƒ

Q21:

Simplify c o t ( 2 7 0 + πœƒ ) ∘ .

  • A βˆ’ πœƒ t a n
  • B βˆ’ πœƒ c o t
  • C c o t πœƒ
  • D t a n πœƒ

Q22:

Simplify s i n ( 2 7 0 + πœƒ ) ∘ .

  • A βˆ’ πœƒ c o s
  • B βˆ’ πœƒ s i n
  • C s i n πœƒ
  • D c o s πœƒ

Q23:

Simplify c o t ( 9 0 + πœƒ ) ∘ .

  • A βˆ’ πœƒ t a n
  • B t a n πœƒ
  • C c o t πœƒ
  • D βˆ’ πœƒ c o t

Q24:

Simplify s e c ( 2 7 0 + πœƒ ) ∘ .

  • A c s c πœƒ
  • B s e c πœƒ
  • C βˆ’ πœƒ s e c
  • D βˆ’ πœƒ c s c

Q25:

Which of the following is equivalent to s i n ( 9 0 βˆ’ πœƒ ) ∘ ?

  • A c o s πœƒ
  • B s i n πœƒ
  • C c s c πœƒ
  • D s e c πœƒ
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