Finding solutions

**Haris** · January 28th 2009, 07:27 AM

Find a solution to

= -10/17 in the interval [

,

] correct to two decimal places.

How would you solve this? Cheers.

**metlx** · January 28th 2009, 08:31 AM

$ cos x = (-\frac{10}{17}) $
$ x_{1} = 126.03^0 + k2\Pi $
$ x_{2} = 233.97^0 + k2\Pi $

$ 19\Pi \leq x_{1,2} + k2\Pi \leq 20\Pi \Rightarrow 3420^0 \leq x_{1,2} + k \times 360^0 \leq 3600^0 $

from that you know that k is 9 because the solution needs to be in the $[19\Pi, 20\Pi]$ interval.

if k = 9
then

$ k2\Pi = 9 \times 2 \times 180^0 = 3240^0 $

$3240^0 + x_{1} \leq 19\Pi$
$20\Pi \geq 3240^0 + x_{2} \geq 19\Pi$

$x_{2} = 233,97^0$ is the solution.

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