Solve each equation over the interval [0°, 360°). Write solutions as exact values or to the nearest tenth, as appropriate.
2sin θ ―1 = csc θ

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Rewrite the given equation \(2\sin \theta - 1 = \csc \theta\) by expressing \(\csc \theta\) in terms of \(\sin \theta\). Recall that \(\csc \theta = \frac{1}{\sin \theta}\), so the equation becomes \(2\sin \theta - 1 = \frac{1}{\sin \theta}\).

Multiply both sides of the equation by \(\sin \theta\) to eliminate the fraction, keeping in mind that \(\sin \theta \neq 0\) to avoid division by zero. This gives \(2\sin^2 \theta - \sin \theta = 1\).

Rearrange the equation to standard quadratic form in terms of \(\sin \theta\): \(2\sin^2 \theta - \sin \theta - 1 = 0\).

Use the quadratic formula to solve for \(\sin \theta\). Recall the quadratic formula is \(x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\), where \(a=2\), \(b=-1\), and \(c=-1\). Substitute these values to find the possible values of \(\sin \theta\).

For each solution of \(\sin \theta\), determine the corresponding angles \(\theta\) in the interval \([0^\circ, 360^\circ)\) by using the inverse sine function and considering the sine function's positive and negative values in different quadrants.

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The problem restricts θ to [0°, 360°), so solutions must be found within one full rotation of the unit circle. Understanding how to find all valid angles in this interval ensures complete and accurate answers.

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