Find a solution to = -10/17 in the interval [, ] correct to two decimal places.
How would you solve this? Cheers.
$\displaystyle
cos x = (-\frac{10}{17})
$
$\displaystyle
x_{1} = 126.03^0 + k2\Pi
$
$\displaystyle
x_{2} = 233.97^0 + k2\Pi
$
$\displaystyle
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 $\displaystyle [19\Pi, 20\Pi]$ interval.
if k = 9
then
$\displaystyle
k2\Pi = 9 \times 2 \times 180^0 = 3240^0
$
$\displaystyle 3240^0 + x_{1} \leq 19\Pi$
$\displaystyle 20\Pi \geq 3240^0 + x_{2} \geq 19\Pi$
$\displaystyle x_{2} = 233,97^0$ is the solution.