Worksheet: Related and Correlated Angle Identities

In this worksheet, we will practice identifying equivalent angles of sine, cosine, and tangent using cofunction identities.

Q1:

Simplify c o s ( 3 6 0 𝜃 ) .

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

Q2:

Simplify t a n ( 1 8 0 𝜃 ) .

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

Q3:

Simplify c o s c o s 𝜃 + ( 1 8 0 𝜃 ) .

Q4:

Simplify t a n ( 3 6 0 𝜃 ) .

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

Q5:

Using the fact that c o s s i n 𝜃 = ( 9 0 𝜃 ) , which of the following is equivalent to c o s 3 5 ?

  • A s i n 1 4 5
  • B s i n 3 5
  • C 3 5 s i n
  • D s i n 5 5
  • E 1 3 5 s i n

Q6:

Which of the following is equivalent to c o s 4 0 ?

  • A 4 0 s i n
  • B s i n 4 0
  • C 1 4 0 s i n
  • D s i n 5 0
  • E s i n 1 4 0

Q7:

Which of the following is equivalent to s i n 2 3 ?

  • A 2 3 c o s
  • B c o s 2 3
  • C 1 2 3 c o s
  • D c o s 6 7
  • E c o s 1 5 7

Q8:

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

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

Q9:

Which of the following is equal to 𝜃 c o s ?

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

Q10:

Which of the following is equivalent to s i n 6 0 ?

  • A 6 0 c o s
  • B c o s 6 0
  • C 1 6 0 c o s
  • D c o s 3 0
  • E c o s 1 2 0

Q11:

Simplify t a n ( 9 0 + 𝜃 ) .

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

Q12:

Which of the following is equal to c o s 𝜃 ?

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

Q13:

Simplify t a n ( 2 7 0 + 𝜃 ) .

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

Q14:

Simplify c o s ( 9 0 𝜃 ) .

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

Q15:

Simplify t a n ( 2 7 0 𝜃 ) .

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

Q16:

Which of the following is equivalent to c o s 3 3 ?

  • A 3 3 s i n
  • B s i n 3 3
  • C 1 3 3 s i n
  • D s i n 5 7
  • E s i n 1 4 7

Q17:

Which of the following is equivalent to s i n 8 0 ?

  • A 8 0 c o s
  • B c o s 8 0
  • C 1 8 0 c o s
  • D c o s 1 0
  • E c o s 1 0 0

Q18:

Simplify c o s ( 9 0 + 𝜃 ) .

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

Q19:

Determine whether the following statement is true or false:

s e c s e c 0 < 4 5 .

  • ATrue
  • BFalse

Q20:

True or false: c s c c s c 7 5 > 6 0 .

  • AFalse
  • BTrue

Q21:

Determine whether the following statement is true or false:

c o s c o s 2 5 < 1 0 .

  • ATrue
  • BFalse

Q22:

Determine whether the following statement is true or false:

s i n s i n 3 0 > 6 0 .

  • AFalse
  • BTrue

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