Question

7. Find the maximum value of the following.
(1) 5 sin x + 12 cos x
(ü) 24 sin x - 7 cos x
(ii) 2 + 3 sin x + 4 cos x
(iv) 8 cos x - 15 sin x - 2.
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Answer 1

Answer:

For this type of problem Always make a diagram of right triangle

After that..

Form the above solution

$13( \frac{5}{13} \sin(x) + \frac{12}{13} \cos(x) ) \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ = 13( \sin(A) \sin(x) + \cos(A) \cos(x) ) \\ \\ = 13( \cos(A</strong><strong> </strong><strong>-</strong><strong> </strong><strong>x)) \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

Now we know the maximum value of cos(x) is 1

$maximum \: \: valu e \: \: of \: \\ \cos(A </strong><strong>-</strong><strong> x) = 1 \\ \\ 13cos(A </strong><strong>-</strong><strong> x) = 13 \times 1 \\ \\ 13cos(A </strong><strong>-</strong><strong> x) = 13$

Try to solve other as same.