Worksheet: Applications of Trigonometric Addition Formula

In this worksheet, we will practice using addition formulas to simplify trigonometric expressions.

Q1:

Given that , where , and , where , find the exact value of .

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Q2:

Simplify .

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Q3:

Find given and where and are acute angles.

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Q4:

Find , given where and where .

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Q5:

Find , given and where and are acute angles.

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Q6:

Given that , where and , where , determine .

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Q7:

Given that , where , and , where , determine .

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Q8:

Find given and where and are two positive acute angles.

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Q9:

Find without using a calculator given and where and are acute angles.

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Q10:

Given that , where , and , where , find .

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Q11:

Find given where and where .

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Q12:

Find given and where and are acute angles.

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Q13:

Find given where and where .

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Q14:

Given that , where , and , where , find the exact value of .

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Q15:

Given that , where , and , where , find the exact value of .

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Q16:

Given that , where , and , where , find the exact value of .

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Q17:

Given that , where , and , where , find the exact value of .

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Q18:

Simplify .

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Q19:

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

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