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# c3 solomon question Watch

1. I need a bit of help fully understanding this question.

7. (a) Express 4 sin x + 3 cos x in the form R sin (x + alpha) where R > 0
and 0 < alpha < pi/2 (4)

(b) State the minimum value of 4 sin x + 3 cos x and the smallest positive
value of x for which this minimum value occurs. (3)

Part a I'm fine with. But on part b, I knew it was -5 since R from the previous question was 5 and I've just followed the pattern from previous exam papers. But I don't actually understand where it comes from.

This is the answer from the mark scheme:

minimum = -5 (B1)
occurs when x + 0.6435 = 3Pi/2, x = 4.07 (3sf)
2. The reason is because when you write what you're doing is scaling and shifting the graph of . As you can tell from the graph, the maximum value can take is 1, and the minimum is -1, so when you scale it by , the maximum and minimum values become .

I can't work out the specifics of where you've gone wrong because your symbols seem to have come out weird, but anyway, when working out the smallest positive value, it's a good idea to make the substitution . Then you need to remember rules like and and so on. Because you're shifting the graph, it might be that one of these gives you a smaller positive value of despite the value of being negative.
3. (Original post by nuodai)
The reason is because when you write what you're doing is scaling and shifting the graph of . As you can tell from the graph, the maximum value can take is 1, and the minimum is -1, so when you scale it by , the maximum and minimum values become .

I can't work out the specifics of where you've gone wrong because your symbols seem to have come out weird, but anyway, when working out the smallest positive value, it's a good idea to make the substitution . Then you need to remember rules like and and so on. Because you're shifting the graph, it might be that one of these gives you a smaller positive value of despite the value of being negative.

Thank you for the help it made complete sense.

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Updated: December 27, 2010
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