Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.

Start Practicing

Worksheet: Evaluating Trigonometric Functions Using Cofunction Identities

Q1:

Find s i n πœƒ given 5 1 ( 9 0 βˆ’ πœƒ ) = 2 4 c o s ∘ where πœƒ is a positive acute angle.

  • A 1 5 1 7
  • B βˆ’ 8 1 7
  • C βˆ’ 1 5 1 7
  • D 8 1 7

Q2:

Which of the following is equal to s i n πœƒ ?

  • A s i n ο€Ό 3 πœ‹ 2 + πœƒ 
  • B s i n ο€» πœ‹ 2 + πœƒ 
  • C c o s ο€» πœ‹ 2 + πœƒ 
  • D c o s ο€Ό 3 πœ‹ 2 + πœƒ 

Q3:

Find the value of t a n ( 2 7 0 βˆ’ πœƒ ) ∘ given c o s πœƒ = βˆ’ 4 5 where 9 0 < πœƒ < 1 8 0 ∘ ∘ .

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

Q4:

Find the value of c o s ( 9 0 + πœƒ ) ∘ given s i n πœƒ = 3 5 where 0 < πœƒ < 9 0 ∘ ∘ .

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

Q5:

Find the value of s i n t a n s i n ( 1 8 0 βˆ’ π‘₯ ) + ( 3 6 0 βˆ’ π‘₯ ) + 4 ( 2 7 0 βˆ’ π‘₯ ) ∘ ∘ ∘ given s i n π‘₯ = 3 5 where 0 < πœƒ < 9 0 ∘ ∘ .

  • A 9 1 2 0
  • B 6 7 2 0
  • C βˆ’ 9 1 2 0
  • D βˆ’ 6 7 2 0

Q6:

Find the value of s i n c o s t a n c o t ( βˆ’ 6 0 ) 3 0 + 5 7 3 3 ∘ ∘ ∘ ∘ giving the answer in its simplest form.

  • A βˆ’ 3 4
  • B βˆ’ 1 4
  • C 3 4
  • D 1 4

Q7:

Find the value of s i n s i n c o s ( 9 0 βˆ’ π‘₯ ) ( π‘₯ ) ( 9 0 βˆ’ 2 π‘₯ ) .

  • A2
  • B1
  • C c o s ( 9 0 βˆ’ π‘₯ )
  • D 1 2
  • E s i n ( 2 π‘₯ )

Q8:

𝐴 𝐡 𝐢 is a right-angled triangle at 𝐡 . Find c o t 𝛼 given c o t πœƒ = 4 3 .

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

Q9:

Simplify c s c ( 2 7 0 βˆ’ πœƒ ) ∘ .

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

Q10:

Simplify c s c ( 2 7 0 + πœƒ ) ∘ .

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

Q11:

Simplify s e c ( 9 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

Q12:

Simplify s e c c o t ο€» βˆ’ πœƒ  ( πœ‹ βˆ’ πœƒ ) πœ‹ 2 .

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

Q13:

Simplify c o s ( 2 7 0 + πœƒ ) ∘ .

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

Q14:

Simplify s i n c o t c s c ο€» πœ‹ 2 βˆ’ πœƒ  ο€» πœ‹ 2 βˆ’ πœƒ  ( πœ‹ βˆ’ πœƒ ) .

Q15:

Simplify c s c ( 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

Q16:

Simplify s i n c o s ο€» βˆ’ πœƒ  ( 2 πœ‹ βˆ’ πœƒ ) πœ‹ 2 .

Q17:

Simplify t a n ( 9 0 βˆ’ πœƒ ) ∘ .

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

Q18:

Simplify s i n c o s πœƒ + ( 2 7 0 + πœƒ ) ∘ .

  • A s i n c o s πœƒ + πœƒ
  • B0
  • C s i n c o s πœƒ βˆ’ πœƒ
  • D 2 πœƒ s i n

Q19:

Simplify c o t ( πœƒ βˆ’ 2 7 0 ) ∘ .

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

Q20:

Simplify s i n c o s ο€» βˆ’ πœƒ  ( βˆ’ πœƒ ) πœ‹ 2 .

Q21:

Simplify c o s ( 2 7 0 βˆ’ πœƒ ) ∘ .

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

Q22:

Simplify c o s ( πœƒ βˆ’ 2 7 0 ) ∘ .

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

Q23:

Simplify c o s ( πœƒ βˆ’ 9 0 ) ∘ .

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

Q24:

Simplify c o t ( πœƒ βˆ’ 9 0 ) ∘ .

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

Q25:

Simplify s e c ( πœƒ βˆ’ 2 7 0 ) ∘ .

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