Worksheet: Evaluating Trigonometric Functions Using Cofunction Identities

In this worksheet, we will practice using cofunction and odd/even identities to find the values of trigonometric functions.

Q1:

Find s i n 𝜃 given 5 1 ( 9 0 𝜃 ) = 2 4 c o s where 𝜃 is a positive acute angle.

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

Q2:

Which of the following is equal to s i n 𝜃 ?

  • A s i n 𝜋 2 + 𝜃
  • B s i n 3 𝜋 2 + 𝜃
  • C c o s 𝜋 2 + 𝜃
  • D c o s 3 𝜋 2 + 𝜃

Q3:

Find the value of t a n ( 2 7 0 𝜃 ) given c o s 𝜃 = 4 5 where 9 0 < 𝜃 < 1 8 0 .

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

Q4:

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

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

Q5:

Find the value of s i n t a n s i n ( 1 8 0 𝑥 ) + ( 3 6 0 𝑥 ) + 7 ( 2 7 0 𝑥 ) given s i n 𝑥 = 3 5 where 0 < 𝜃 < 9 0 .

  • A 1 3 9 2 0
  • B 2 3 4
  • C 2 3 4
  • D 1 3 9 2 0

Q6:

Find the value of s i n c o s t a n c o t ( 6 0 ) 3 0 + 5 7 3 3 giving the answer in its simplest form.

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

Q7:

Find the value of s i n s i n c o s ( 9 0 𝑥 ) ( 𝑥 ) ( 9 0 2 𝑥 ) .

  • A s i n ( 2 𝑥 )
  • B 1 2
  • C1
  • D c o s ( 9 0 𝑥 )
  • E2

Q8:

𝐴 𝐵 𝐶 is a right-angled triangle at 𝐵 . Find c o t 𝛼 given c o t 𝜃 = 4 3 .

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

Q9:

Simplify c s c ( 2 7 0 𝜃 ) .

  • A 𝜃 s e c
  • B s e c 𝜃
  • C c s c 𝜃
  • D 𝜃 c s c

Q10:

Simplify c s c ( 2 7 0 + 𝜃 ) .

  • A 𝜃 c s c
  • B c s c 𝜃
  • C 𝜃 s e c
  • D s e c 𝜃

Q11:

Simplify s e c ( 9 0 + 𝜃 ) .

  • A s e c 𝜃
  • B c s c 𝜃
  • C 𝜃 s e c
  • D 𝜃 c s c

Q12:

Simplify s e c c o t 𝜃 ( 𝜋 𝜃 ) .

  • A s e c 𝜃
  • B 𝜃 c s c
  • C 𝜃 s e c
  • D 𝜃 c o s

Q13:

Simplify c o s ( 2 7 0 + 𝜃 ) .

  • A c o s 𝜃
  • B 𝜃 c o s
  • C 𝜃 s i n
  • D s i n 𝜃

Q14:

Simplify s i n c o t c s c 𝜋 2 𝜃 𝜋 2 𝜃 ( 𝜋 𝜃 ) .

Q15:

Simplify c s c ( 9 0 + 𝜃 ) .

  • A s i n 𝜃
  • B c s c 𝜃
  • C s e c 𝜃
  • D c o s 𝜃

Q16:

Simplify s i n c o s 𝜃 ( 2 𝜋 𝜃 ) .

Q17:

Simplify t a n ( 9 0 𝜃 ) .

  • A c o t 𝜃
  • B t a n 𝜃
  • C s e c 𝜃
  • D c s c 𝜃

Q18:

Simplify s i n c o s 𝜃 + ( 2 7 0 + 𝜃 ) .

  • A s i n c o s 𝜃 𝜃
  • B s i n c o s 𝜃 + 𝜃
  • C0
  • D 2 𝜃 s i n

Q19:

Simplify c o t ( 𝜃 2 7 0 ) .

  • A 𝜃 c o t
  • B 𝜃 t a n
  • C t a n 𝜃
  • D c o t 𝜃

Q20:

Simplify s i n c o s 𝜃 ( 𝜃 ) .

Q21:

Simplify c o s ( 2 7 0 𝜃 ) .

  • A c o s 𝜃
  • B s i n 𝜃
  • C 𝜃 c o s
  • D 𝜃 s i n

Q22:

Simplify c o s ( 𝜃 2 7 0 ) .

  • A 𝜃 s i n
  • B 𝜃 c o s
  • C c o s 𝜃
  • D s i n 𝜃

Q23:

Simplify c o s ( 𝜃 9 0 ) .

  • A c o s 𝜃
  • B s i n 𝜃
  • C 𝜃 s i n
  • D 𝜃 c o s

Q24:

Simplify c o t ( 𝜃 9 0 ) .

  • A t a n 𝜃
  • B 𝜃 c o t
  • C 𝜃 t a n
  • D c o t 𝜃

Q25:

Simplify s e c ( 𝜃 2 7 0 ) .

  • A 𝜃 s e c
  • B 𝜃 c s c
  • C 𝜃 c s c
  • D s e c 𝜃

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