Given that cosTheta =-0.2563 determine all possible values of Theta ,0^circ leqslant Theta leqslant 360^circ

## Step 1: Find the reference angle<br />### We are given $\cos(\Theta) = -0.2563$. Since the cosine is negative, $\Theta$ must be in the second or third quadrant. First, we find the reference angle $\alpha$ such that $\cos(\alpha) = 0.2563$. Using a calculator, we find $\alpha = \arccos(0.2563) \approx 75.16^\circ$.<br /><br />## Step 2: Calculate the angles in the second and third quadrants<br />### For the second quadrant, $\Theta = 180^\circ - \alpha = 180^\circ - 75.16^\circ = 104.84^\circ$.<br />### For the third quadrant, $\Theta = 180^\circ + \alpha = 180^\circ + 75.16^\circ = 255.16^\circ$.