Trigonometric Preliminaries Project Help (1 Viewer)

[nimrod_dookie]

Hi. I am a South Australian student currently doing my SACE Certificate. I don't know how similar our advanced maths courses are but hopefully someone here can help me. I am doing a project where I have gotten to a certain point in the second question and I can't get any further.

The question is:

Farmer Carter observed that Daisy's daily milk production was periodic and could be modelled by the function:

P(t) =ksin(Ϊ/6t + Θ)+11.2 where k is greater than 0 and 0<Θ<2Ϊ)

1. Using the addition formula for sin (A+B), write and alternative expression for P(t).

2. By equating this expression for P(t) to the expression found in question 1 (P(t)=10cos(Ϊ/6t)+5sin(Ϊ/6t)+11.2), state a value for ksinΘ and kcosΘ.

ksinΘ=10 and kcosΘ=5 (my handwriting wasn't given justice when scanned)

3. Using the identity sin^2A+cos^2A=1, find k in simplest surd form. (This is the question I am having problems with)

To see what I have done for parts 1 and 2 go to http://spaces.msn.com/listerineicecream/photos/?_c02_owner=1

My teacher has told me those parts are correct. Although with part 1, if anyone can simplify that, it would also be great. Any help would be greatly appreciated.

Thanking you in advance

 

[SeDaTeD]

If ksinΘ=10 and kcosΘ=5, then
k^2sin^2Θ=100 and k^2cos^2Θ=25
k^2sin^2Θ + k^2cos^2Θ=100 + 25 = 125
k^2(sin^2Θ + cos^2Θ) = k^2 = 125
k = 5sqrt5

 

[nimrod_dookie]

:wave: Thankyou so much .

 

[nimrod_dookie]

And if I was to work out θ by substuting the value of k into the previous equations, i would work it out using radians wouldnt I?

 

[SeDaTeD]

Yes, radians.