Lesson Worksheet: Related and Correlated Angle Identities Mathematics

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:

True or false: csccsc75>60.

  • AFalse
  • BTrue

Q20:

Simplify sin(360𝜃).

  • A𝜃sin
  • Bcos𝜃
  • C𝜃cos
  • Dsin𝜃

Q21:

Consider the unit circle shown.

The line segment 𝑂𝑁 is obtained by rotating 𝑂𝑀 by an angle of 𝜋2 about 𝑂. The line segment 𝑂𝑁 is obtained by reflecting 𝑂𝑁 in the 𝑦-axis.

What angle does the line segment 𝑂𝑁 make with the positive 𝑥-axis?

  • A𝜋22𝜃
  • B2𝜃
  • C𝜋𝜃
  • D𝜋2𝜃
  • E𝜋2+𝜃

What are the coordinates of the points 𝑁 and 𝑁?

  • A𝑁(𝜃sin, cos𝜃), 𝑁(𝜃sin, cos𝜃)
  • B𝑁(𝜃,𝜃)sincos, 𝑁(𝜃,𝜃)sincos
  • C𝑁(𝜃,𝜃)sincos, 𝑁(𝜃,𝜃)sincos
  • D𝑁(𝜃,𝜃)sincos, 𝑁(𝜃,𝜃)sincos
  • E𝑁(𝜃,𝜃)cossin, 𝑁(𝜃,𝜃)cossin

Write sin𝜋2𝜃 and cos𝜋2𝜃 in terms of sin𝜃 and cos𝜃.

  • Acoscos𝜋2𝜃=𝜃, sinsin𝜋2𝜃=𝜃
  • Bcossin𝜋2𝜃=𝜃, sincos𝜋2𝜃=𝜃
  • Ccossin𝜋2𝜃=𝜃, sincos𝜋2𝜃=𝜃
  • Dcoscos𝜋2𝜃=𝜃, sinsin𝜋2𝜃=𝜃
  • Ecossin𝜋2𝜃=𝜃, sincos𝜋2𝜃=𝜃

Q22:

Simplify sin(𝜃270).

  • Asin𝜃
  • B𝜃cos
  • Ccos𝜃
  • D𝜃sin

Q23:

In the figure, points 𝑀(𝜃,𝜃)cossin and 𝑁 lie on the unit circle, and 𝐴𝑂𝑁=𝜋+𝜃.

Express the values of sine, cosine, and tangent of 𝜋+𝜃 in terms of their values for 𝜃. Check whether this is valid for all values of 𝜃.

  • Acoscossinsintantan(𝜋+𝜃)=𝜃,(𝜋+𝜃)=𝜃,(𝜋+𝜃)=𝜃
  • Bcoscossinsintantan(𝜋+𝜃)=𝜃,(𝜋+𝜃)=𝜃,(𝜋+𝜃)=𝜃
  • Ccoscossinsintantan(𝜋+𝜃)=𝜃,(𝜋+𝜃)=𝜃,(𝜋+𝜃)=𝜃
  • Dcoscossinsintantan(𝜋+𝜃)=𝜃,(𝜋+𝜃)=𝜃,(𝜋+𝜃)=𝜃
  • Ecoscossinsintantan(𝜋+𝜃)=𝜃,(𝜋+𝜃)=𝜃,(𝜋+𝜃)=𝜃

Q24:

Which of the following is equal to sin𝜃?

  • Acos𝜋2+𝜃
  • Bcos3𝜋2+𝜃
  • Csin3𝜋2+𝜃
  • Dsin𝜋2+𝜃

Q25:

The given figure shows a right-angled triangle with its complementary angles labeled as 𝜃 and 90𝜃.

Work out the value of cos𝜃.

  • A𝑏𝑐
  • B𝑐𝑏
  • C𝑐𝑎
  • D𝑎𝑐
  • E𝑎𝑏

Work out the value of sin𝜃.

  • A𝑐𝑏
  • B𝑎𝑏
  • C𝑎𝑐
  • D𝑐𝑎
  • E𝑏𝑐

Work out the value of sin(90𝜃).

  • A𝑐𝑎
  • B𝑎𝑏
  • C𝑐𝑏
  • D𝑏𝑐
  • E𝑎𝑐

Work out the value of cos(90𝜃).

  • A𝑐𝑏
  • B𝑐𝑎
  • C𝑎𝑏
  • D𝑏𝑐
  • E𝑎𝑐

What conclusion can be drawn about the value of sin𝜃 and cos(90𝜃)?

  • Asincos𝜃=1(90𝜃).
  • BThey are equal.
  • Csincos𝜃=2(90𝜃).
  • Dsincos𝜃=1(90𝜃).
  • Esincos𝜃=(90𝜃).

What conclusion can be drawn about the value of cos𝜃 and sin(90𝜃)?

  • Acossin𝜃=(90𝜃).
  • BThey are equal.
  • Ccossin𝜃=2(90𝜃).
  • Dcossin𝜃=1(90𝜃).
  • Ecossin𝜃=1(90𝜃).

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.