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December 14th, 2017, 05:18 PM   #1
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Linear dependence question

Let $\displaystyle f_1(x) = sin x,~ f_2(x) = cos(x + \frac{\pi}{6}), and~ f_3(x) = sin(x - \frac{\pi}{4}) $ for $\displaystyle 0 <= x <= 2\pi$. Show that
{ $\displaystyle f_1, f_2, f_3$ } is linearly dependent by finding constants c and k such that $\displaystyle cf_1 - 2f_2 - kf3 = 0 $.

what is c and k?
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December 14th, 2017, 06:53 PM   #2
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Here is a hint:

http://www2.clarku.edu/~djoyce/trig/sumformulas.jpg
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December 14th, 2017, 07:00 PM   #3
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