Miscellaneous Questions (1 Viewer)

pomsky · Jul 12, 2015

Find the general solution of the equation $sin3x + sinx = cosx$

VBN2470 · Jul 12, 2015

Note that $\sin{3x}=3\sin{x}-4\sin^3{x}$ , so that you will have to solve the trig. equation $4\sin{x}-4\sin^3{x}=\cos{x}$ after substituition. This will turn out be $\cos{x}(2\sin{2x}-1)=0$ (after re-arranging and simplifying), making it easy to find your general solutions.

mreditor16 · Jul 12, 2015

VBN2470 said:
Note that $\sin{3x}=3\sin{x}-4\sin^3{x}$ , so that you will have to solve the trig. equation $4\sin{x}-4\sin^3{x}=\cos{x}$ after substituition. This will turn out be $\cos{x}(2\sin{2x}-1)=0$ (after re-arranging and simplifying), making it easy to find your general solutions.

OP, you would probably be expected to show the bolded part, by applying sin(alpha+beta)=sin(alpha)cos(beta)+cos(alpha)sin(beta) - letting alpha=2x and beta=x (or vice versa) and then going from there....

pomsky · Jul 12, 2015

The probability that it rains on any particular day in Brisbane is $\frac{2}{3}.$ What is the probability that it will rain on only two days during a whole week in London and these two days are consecutive?

InteGrand · Jul 12, 2015

pomsky said:
The probability that it rains on any particular day in Brisbane is $\frac{2}{3}.$ What is the probability that it will rain on only two days during a whole week in London and these two days are consecutive?

$The number of ways to select the two consecutive days of rain in the 7-day week is clearly just 6 (i.e. the first day of rain could be on Day 1 or Day 2 or ... or Day 6). The probability of each of these two-day rain occurrences is $p^2 q^5$, where $p=\frac{2}{3},q = 1-p =\frac{1}{3}.$ Hence the required probability is $6p^2 q^5$.$

(Also, the Q says Brisbane and London lol.)

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Miscellaneous Questions (1 Viewer)

pomsky

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pomsky

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InteGrand

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