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).

  • A𝜃cos
  • Bcos𝜃
  • Csin𝜃
  • D𝜃sin

Q2:

Simplify tan(180𝜃).

  • A𝜃tan
  • Btan𝜃
  • Ccot𝜃
  • D𝜃cot

Q3:

Simplify coscos𝜃+(180𝜃).

Q4:

Simplify tan(360𝜃).

  • Atan𝜃
  • B𝜃tan
  • Ccot𝜃
  • D𝜃cot

Q5:

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

  • A135sin
  • B35sin
  • Csin35
  • Dsin145
  • Esin55

Q6:

Which of the following is equivalent to cos40?

  • Asin140
  • B40sin
  • Csin50
  • Dsin40
  • E140sin

Q7:

Which of the following is equivalent to sin23?

  • A23cos
  • Bcos157
  • Ccos23
  • D123cos
  • Ecos67

Q8:

Which of the following is equal to 𝜃sin?

  • Acos𝜋2+𝜃
  • Bsin3𝜋2+𝜃
  • Csin𝜋2+𝜃
  • Dcos3𝜋2+𝜃

Q9:

Which of the following is equal to 𝜃cos?

  • Asin3𝜋2+𝜃
  • Bsin𝜋2+𝜃
  • Ccos3𝜋2+𝜃
  • Dcos𝜋2+𝜃

Q10:

Which of the following is equivalent to sin60?

  • Acos120
  • B160cos
  • C60cos
  • Dcos60
  • Ecos30

Q11:

Simplify tan(90+𝜃).

  • Acot𝜃
  • B𝜃tan
  • Ctan𝜃
  • D𝜃cot

Q12:

Which of the following is equal to cos𝜃?

  • Asin𝜋2+𝜃
  • Bcos𝜋2+𝜃
  • Ccos3𝜋2+𝜃
  • Dsin3𝜋2+𝜃

Q13:

Simplify tan(270+𝜃).

  • Acot𝜃
  • B𝜃cot
  • C𝜃tan
  • Dtan𝜃

Q14:

Simplify cos(90𝜃).

  • Asin𝜃
  • Bcos𝜃
  • Csec𝜃
  • Dcsc𝜃

Q15:

Simplify tan(270𝜃).

  • Acot𝜃
  • B𝜃tan
  • Ctan𝜃
  • D𝜃cot

Q16:

Which of the following is equivalent to cos33?

  • A33sin
  • Bsin147
  • C133sin
  • Dsin33
  • Esin57

Q17:

Which of the following is equivalent to sin80?

  • Acos100
  • Bcos10
  • C180cos
  • D80cos
  • Ecos80

Q18:

Simplify cos(90+𝜃).

  • Asin𝜃
  • B𝜃sin
  • Ccsc𝜃
  • D𝜃csc

Q19:

Determine whether the following statement is true or false:

secsec0<45.

  • ATrue
  • BFalse

Q20:

True or false: csccsc75>60.

  • AFalse
  • BTrue

Q21:

Determine whether the following statement is true or false:

coscos25<10.

  • ATrue
  • BFalse

Q22:

Determine whether the following statement is true or false:

sinsin30>60.

  • AFalse
  • BTrue

Q23:

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

  • A15
  • B54
  • C45
  • D15
  • E45

Q24:

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

  • A23
  • B13
  • C23
  • D1
  • E13

Q25:

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

  • A45
  • B54
  • C45
  • D54

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