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Solve sinusoidal equations (basic)

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Jamie tried to solve the following equation, where x is in radians to the nearest hundredth, in the interval from minus, pi to pi, but she made a mistake.
cosine, left parenthesis, x, right parenthesis, equals, minus, 0, point, 08
Here is Jamie's work.
cos1(cos(x))=cos1(0.08)x1.65Using cos(x)=cos(x+2π)x1.65+2πnx4.631.657.93Using cos(x)=cos(πx)and cos(x)=cos(x+2π)x1.49+2πnx4.791.497.77\begin{array}{rcl} \cos^{-1}(\cos (x)) &= &\cos^{-1}( -0.08 )\\\\ x &\approx & 1.65\\\\ \swarrow&&\searrow\\\\ \begin{aligned} &\blueE{\text{Using }\cos(x)=\cos(x+2\pi)}\\\\ x &\approx 1.65+ 2\pi n\\\\ x &\approx \ldots -4.63\text{, }1.65\text{, }7.93\ldots \end{aligned}&& \begin{aligned} &\purpleD{\text{Using }\cos(x)=\cos(\pi-x)}\\\\ &\purpleD{\text{and }\cos(x)=\cos(x+2\pi)}\\\\ x &\approx 1.49 + 2\pi n\\\\ x &\approx \ldots -4.79\text{, }1.49\text{, }7.77\ldots \end{aligned} \end{array}
The solutions to x in the interval from minus, pi to pi are x, approximately equals, 1, point, 49 and x, approximately equals, 1, point, 65.
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