Worksheet: Using Cofunction Identities to Find θ

In this worksheet, we will practice using the cofunction identities to find the angle θ.

Q1:

Find 𝜃 in degrees given c o s s i n 1 5 3 1 5 = 𝜃 where 𝜃 is an acute angle.

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

Q2:

Find 𝜃 in degrees given c s c c s c 3 2 7 4 5 = 𝜃 where 𝜃 is an acute angle.

  • A 5 7 4 5
  • B 2 2 1 5
  • C 4 7 4 5
  • D 3 2 1 5

Q3:

Find the value of 𝑥 given t a n c o t 7 8 = 𝑥 .

Q4:

Simplify s i n ( 𝜃 2 7 0 ) .

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

Q5:

Which of the following is the general solution of the equation c s c s e c 6 𝜃 = 3 𝜃 ?

  • A 𝜋 9 + 𝜋 𝑛 9 or 𝜋 3 𝜋 𝑛 3 , where 𝑛
  • B 2 𝜋 9 + 2 𝜋 𝑛 9 or 2 𝜋 3 + 2 𝜋 𝑛 3 , where 𝑛
  • C 𝜋 1 8 2 𝜋 𝑛 9 or 𝜋 6 + 2 𝜋 𝑛 3 , where 𝑛
  • D 𝜋 1 8 + 2 𝜋 𝑛 9 or 𝜋 6 + 2 𝜋 𝑛 3 , where 𝑛

Q6:

𝐴 𝐵 𝐶 𝐷 is a trapezium where 𝑚 𝐴 = 𝑚 𝐷 = 9 0 , 𝐶 𝐷 = 2 1 c m , 𝐴 𝐷 = 1 2 c m , and 𝐴 𝐵 = 3 0 c m . Find s i n 𝜃 .

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

Q7:

Simplify s i n ( 2 7 0 𝜃 ) .

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

Q8:

Simplify s i n ( 9 0 + 𝜃 ) .

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

Q9:

Simplify s i n ( 2 7 0 + 𝜃 ) .

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

Q10:

Which of the following is equivalent to s i n ( 9 0 𝜃 ) ?

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

Q11:

Simplify s e c t a n t a n 𝜃 𝜃 ( 2 7 0 + 𝜃 ) .

  • A s e c 𝜃
  • B c s c 𝜃
  • C 𝜃 s i n 2
  • D 𝜃 s e c

Q12:

𝐴 𝐵 𝐶 𝐷 is a square where 9 𝐷 𝐹 = 1 0 𝐹 𝐶 . Find the exact value of c o s 𝜃 .

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

Q13:

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

Q14:

Simplify c o t ( 9 0 𝜃 ) .

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

Q15:

Simplify c o t ( 2 7 0 𝜃 ) .

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

Q16:

Simplify s e c ( 2 7 0 𝜃 ) .

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

Q17:

Simplify c s c ( 9 0 𝜃 ) .

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

Q18:

Simplify s e c ( 9 0 𝜃 ) .

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

Q19:

Simplify c o t ( 2 7 0 + 𝜃 ) .

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

Q20:

Simplify c o t ( 9 0 + 𝜃 ) .

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

Q21:

Simplify s e c ( 2 7 0 + 𝜃 ) .

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

Q22:

Find the value of c o s c o s c o s c o s c o s 2 2 2 2 2 𝜋 2 0 + 3 𝜋 2 0 + 5 𝜋 2 0 + 7 𝜋 2 0 + 9 𝜋 2 0 .

Q23:

Find the value of 𝑥 given c s c s e c 2 7 = 𝑥 .

Q24:

Find the value of 𝑥 given c s c s e c 8 0 = 𝑥 .

Q25:

Find 𝜃 in degrees given s e c c s c 1 6 4 = 𝜃 where 𝜃 is an acute angle.

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

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