If cos x = -0.750 and sin ≈ 0.6614, then tan x/2 ≈ .

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Identify the given values: \(\cos x = -0.750\) and \(\sin x \approx 0.6614\).

Recall the half-angle formula for tangent: \(\tan \frac{x}{2} = \frac{1 - \cos x}{\sin x}\) or \(\tan \frac{x}{2} = \frac{\sin x}{1 + \cos x}\). Choose the form that avoids division by zero or undefined expressions based on the quadrant of \(x\).

Since \(\cos x\) is negative and \(\sin x\) is positive, \(x\) lies in the second quadrant. For \(x\) in the second quadrant, use the formula \(\tan \frac{x}{2} = \frac{1 - \cos x}{\sin x}\) to ensure the correct sign.

Substitute the given values into the chosen formula: \(\tan \frac{x}{2} = \frac{1 - (-0.750)}{0.6614} = \frac{1 + 0.750}{0.6614}\).

Simplify the expression to find the approximate value of \(\tan \frac{x}{2}\).

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