// Numbas version: exam_results_page_options {"name": "Write as a single trigonometric ratio", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"showfrontpage": false, "preventleave": false, "allowregen": true}, "question_groups": [{"questions": [{"type": "question", "advice": "

R\\cos(x+a) = R\\cos{x}\\cos{a}-R\\sin{x}\\sin{a}

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R\\cos{a}=8 and R\\sin{a}=6

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R^2=100 \\Rightarrow R=10

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\\tan{a}=\\frac{3}{2} \\Rightarrow a=0.6435...

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A=10\\cos(x+0.64)

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max(A)=10

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Addition Formulas in Trigonometry. Range of Sinusoidal functions.

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You should find the exact value of $R$ and write $a$ correct to two decimal places.

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State the Maximum possible value of $A$

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Express $$8\\cos{x}-6\\sin{x}$$ in the form $$R\\cos{x+a}$$ where $R\\in \\mathbb{R}$ and $-\\pi<a<\\pi$.

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