# Lesson Worksheet: Double-Angle and Half-Angle Identities Mathematics

In this worksheet, we will practice using the Pythagorean identity and double-angle formulas to evaluate trigonometric values.

Q1:

Find the value of given where without using a calculator.

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• D

Q2:

Find the value of given without using a calculator.

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• D

Q3:

Find, without using a calculator, the value of given where .

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• D

Q4:

Find the value of given where without using a calculator.

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• D

Q5:

Find, without using a calculator, the value of given where .

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• E

Q6:

Find, without using a calculator, the value of given where .

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• D

Q7:

is a triangle where . Find the value of .

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• D

Q8:

Find the value of given where .

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Q9:

Find, without using a calculator, given where .

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• D16

Q10:

Which of the following is equal to ?

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Q11:

Use the addition formula to find an expression for .

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Q12:

Find the value of given where without using a calculator.

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• D

Q13:

Find the value of and then without using a calculator.

• A, 6
• B, 6
• C, 8
• D, 16

Q14:

Find the value of given .

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Q15:

Find, without using a calculator, the value of given where .

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Q16:

Use the addition formula to find an expression for .

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• E

Q17:

Which of the following is equal to ?

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• E

Q18:

Using the half angle formulas, or otherwise, find the exact value of .

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• E

Q19:

Find the value of without using a calculator.

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• D

Q20:

Evaluate without using a calculator.

• A18
• B36
• C
• D1

Q21:

Simplify .

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Q22:

is a triangle, where the ratio between its lengths , , and is . Find .

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Q23:

Find the value of without using a calculator.

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Q24:

Calculate .

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Q25:

Find, without using a calculator, the value of given where .

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• D