Compound angles Watch

Tynos
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Help with these please, i dont understand what the max/min are.

Thanks!
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Hasufel
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the question is really after the amplitude of the expression. (to be precise, the lowest value and the highest value - the lowest will be the negative of the highest)

I will do a) just to demonstrate the idea.

We might be able to notice, straight away, that a) is of the form  Cos(A-B) (here, A=x, B= Pi/6. In which case the amplitude is 1.

But, what if we didn`t?

we use the fact that we have a cos function first, followed by a + sign separating terms to suppose that we have something of the form  R \times Cos(x-\alpha)
where R is the amplitude.

We then expand this to read (Rcos( \alpha))cos(x)+(Rsin( \alpha))sin(x)

so that, Rcos( \alpha)= \frac{\sqrt{3}}{2} and Rsin( \alpha)= \frac{1}{2} from which, tan( \alpha) = \frac{1}{\sqrt{3}}=> \alpha = \frac{\pi}{6}

Now, R= \sqrt{(\frac{\sqrt{3}}{2})^{2}+(  \frac{1}{2})^{2}}=1

so the actual expression is equal to: Cos(x-\frac{\pi}{6})

Do this for b, c, and d, picking the most suitable form of cos/sin(A+/-B) opr the expression

for b) take out a factor of 3 first, and a factor of 4 out of d).
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Tynos
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(Original post by Hasufel)
the question is really after the amplitude of the expression. (to be precise, the lowest value and the highest value - the lowest will be the negative of the highest)

I will do a) just to demonstrate the idea.

We might be able to notice, straight away, that a) is of the form  Cos(A-B) (here, A=x, B= Pi/6. In which case the amplitude is 1.

But, what if we didn`t?

we use the fact that we have a cos function first, followed by a + sign separating terms to suppose that we have something of the form  R \times Cos(x-\alpha)
where R is the amplitude.

We then expand this to read (Rcos( \alpha))cos(x)+(Rsin( \alpha))sin(x)

so that, Rcos( \alpha)= \frac{\sqrt{3}}{2} and Rsin( \alpha)= \frac{1}{2} from which, tan( \alpha) = \frac{1}{\sqrt{3}}=> \alpha = \frac{\pi}{6}

Now, R= \sqrt{(\frac{\sqrt{3}}{2})^{2}+(  \frac{1}{2})^{2}}=1

so the actual expression is equal to: Cos(x-\frac{\pi}{6})

Do this for b, c, and d, picking the most suitable form of cos/sin(A+/-B) opr the expression

for b) take out a factor of 3 first, and a factor of 4 out of d).
Ah, ok thanks.
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