The graph of $y=\cos x$ for $0^{\circ} \leq x \leq 360^{\circ}$ is shown below.
Calculate the two solutions to $\cos x=0.52$ for $0^{\circ} \leq x \leq 360^{\circ}$. Give your answers to 1 d.p.

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Answer

$\boxed{x_1 \approx 58.7^\circ, x_2 \approx 301.3^\circ}$

Steps

Step 1 ：Find the two angles x in the range of 0 to 360 degrees for which the cosine of x is equal to 0.52.

Step 2 ：Use the inverse cosine function (acos) to find the angles.

Step 3 ：$x_1 = \arccos(0.52)$

Step 4 ：$x_1 \approx 58.7^\circ$

Step 5 ：$x_2 = 360^\circ - x_1$

Step 6 ：$x_2 \approx 301.3^\circ$

Step 7 ：$\boxed{x_1 \approx 58.7^\circ, x_2 \approx 301.3^\circ}$