Solving the system: \(\displaystyle{11}{{\cos{{x}}}_{{1}}+}{12}{{\cos{{x}}}_{{2}}=}{0}\) and \(\displaystyle{11}{{\sin{{x}}}_{{1}}+}{12}{{\sin{{x}}}_{{2}}=}{17}\)

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ezpimpin6988ok1n

Answered question

2022-03-31

Solving the system: 11cosx1+12cosx2=0 and 11sinx1+12sinx2=17

Answer & Explanation

Adan Berry

Adan Berry

Beginner2022-04-01Added 12 answers

From these one gets 11eix1+12eix2=17i. So the points 0, 11eix1 and 17i form a triangle in the Argand diagram with side-lengths 11, 12 and 17. One can find the possible values of 11eix1 by intersecting the circle centre 0 and radius 11 with the circle centre 17i and radius 12.
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uqhekekocj8f

Beginner2022-04-02Added 8 answers

Hint:
11cos(x1)+12cos(x2)=011cos(x1)=12cos(x2)
11sin(x1)+12sin(x2)=1711sin(x1)=1712sin(x2)
Now square both equations and add them then replace cos2(xi)+sin2(xi)=1
112(cos2(x1)+sin2(x1))=122cos2(x2)+17221712sin(x2)+122sin2(x2)
112=122+17221712sin(x2)

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