Worksheet: Related and Correlated Angle Identities

In this worksheet, we will practice writing trigonometric functions, like sine, cosine, and tangent, and their reciprocals in terms of cofunctions and use their properties to compare two trigonometric functions.

Q1:

Simplify cos(360𝜃).

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

Q2:

Simplify tan(180𝜃).

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

Q3:

Simplify coscos𝜃+(180𝜃).

Q4:

Simplify tan(360𝜃).

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

Q5:

Using the fact that cossin𝜃=(90𝜃), which of the following is equivalent to cos35?

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

Q6:

Which of the following is equivalent to cos40?

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

Q7:

Which of the following is equivalent to sin23?

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

Q8:

Which of the following is equal to 𝜃sin?

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

Q9:

Which of the following is equal to 𝜃cos?

  • 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

Q10:

Which of the following is equivalent to sin60?

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

Q11:

Simplify tan(90+𝜃).

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

Q12:

Which of the following is equal to cos𝜃?

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

Q13:

Simplify tan(270+𝜃).

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

Q14:

Simplify cos(90𝜃).

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

Q15:

Simplify tan(270𝜃).

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

Q16:

Which of the following is equivalent to cos33?

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

Q17:

Which of the following is equivalent to sin80?

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

Q18:

Simplify cos(90+𝜃).

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

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: csccsc75>60.

  • 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

Q23:

Given that sin𝜃=45, find the value of sin(𝜋+𝜃).

  • A 1 5
  • B 5 4
  • C 4 5
  • D 1 5
  • E 4 5

Q24:

Given that cos𝜃=23, find the value of cos(𝜋+𝜃).

  • A 2 3
  • B 1 3
  • C 2 3
  • D1
  • E 1 3

Q25:

Find csc𝛽 given 𝛼 and 𝛽 are two complementary angles where sec𝛼=54.

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

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