# Worksheet: Applications of Trigonometric Addition Formula

Q1:

Simplify .

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Q2:

Simplify .

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Q3:

Using the relation , find an expression for in terms of and which holds when .

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Q4:

Simplify .

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Q5:

Simplify .

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Q6:

Simplify .

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Q7:

Simplify .

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Q8:

Simplify .

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Q9:

Simplify .

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Q10:

Simplify .

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Q11:

Simplify .

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Q12:

In the given figure, is a rectangle and the length of is 1.

Find the lengths of and in terms of and .

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Find in terms of and . Hence find the lengths of and .

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By considering a suitable angle, find the lengths of and .

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Use your answers to the previous parts of the question to find expressions for and .

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Q13:

In the figure, which triangles are similar?

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• B , , , and
• C , , and
• D , , , and
• E , , and

Given that , find expressions for the lengths of , , , and .

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• C , , ,
• D , , ,
• E , , ,

Find an expression for .

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Q14:

Consider the given figure.

Find the lengths and in terms of and .

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• E ,

Find the lengths , , , and in terms of and .

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• B , , ,
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• D , , ,

By writing and in terms of , , , and , find expressions for and in terms of , , , and .

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• D ,

Q15:

Using the relation , find an expression for in terms of and which holds when .

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Q16:

Simplify .

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Q17:

Simplify .

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Q18:

Simplify .

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Q19:

Simplify .

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