# 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 .

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• D

Q2:

Simplify .

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• D

Q3:

Simplify .

Q4:

Simplify .

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• D

Q5:

Using the fact that , which of the following is equivalent to ?

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• E

Q6:

Which of the following is equivalent to ?

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• E

Q7:

Which of the following is equivalent to ?

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• E

Q8:

Which of the following is equal to ?

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• D

Q9:

Which of the following is equal to ?

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• D

Q10:

Which of the following is equivalent to ?

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• E

Q11:

Simplify .

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• D

Q12:

Which of the following is equal to ?

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• D

Q13:

Simplify .

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Q14:

Simplify .

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Q15:

Simplify .

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• D

Q16:

Which of the following is equivalent to ?

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• E

Q17:

Which of the following is equivalent to ?

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• E

Q18:

Simplify .

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Q19:

True or false: .

• AFalse
• BTrue

Q20:

Simplify .

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• D

Q21:

Consider the unit circle shown. The line segment is obtained by rotating by an angle of about . The line segment is obtained by reflecting in the -axis.

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

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What are the coordinates of the points and ?

• A, , ,
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• E,

Write and in terms of and .

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• D,
• E,

Q22:

Simplify .

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Q23:

In the figure, points and lie on the unit circle, and . Express the values of sine, cosine, and tangent of in terms of their values for . Check whether this is valid for all values of .

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• E

Q24:

Which of the following is equal to ?

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• D

Q25:

The given figure shows a right-angled triangle with its complementary angles labeled as and . Work out the value of .

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• E

Work out the value of .

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• E

Work out the value of .

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• E

Work out the value of .

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What conclusion can be drawn about the value of and ?

• A.
• BThey are equal.
• C.
• D.
• E.

What conclusion can be drawn about the value of and ?

• A.
• BThey are equal.
• C.
• D.
• E.