Trigonometric equations (2)

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May 14th 2006, 04:43 PM
LilDragonfly

Trigonometric equations (2)

Find the general solution of:

5cot(3x + 4) = 1
May 14th 2006, 06:55 PM
ThePerfectHacker

Quote:

Originally Posted by LilDragonfly

Find the general solution of:

5cot(3x + 4) = 1

Thus,
$\cot (3x+4)=\frac{1}{5}$
Let,
$y=3x+4$
Then,
$\cot y=\frac{1}{5}$
which you find that,
$y=\cot^{-1}(1/5)+\pi k$
Thus,
$3x+4=\cot^{-1}(1/5)+\pi k$
Thus,
$x=\frac{1}{3}\cot^{-1}(1/5)+\frac{\pi k}{3}-4$

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