Use a calculator to find a decimal approximation for the following expression. $$ \sec 99^{\circ} 35^{\prime} $$ $$ \sec 99^{\circ} 35^{\prime}=\square $$ (Type an integer or decimal rounded to four decimal places as needed.)

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$$ \sec 99^{\circ} 35^{\prime} \approx -10.0000 $$ To find the decimal approximation for $$\sec 99^{\circ} 35^{\prime}$$, we first need to convert the angle from degrees and minutes to decimal degrees. 1. Convert $$35^{\prime}$$ (minutes) to degrees: $$ 35^{\prime} = \frac{35}{60} = 0.5833^{\circ} $$ 2. Add this to $$99^{\circ}$$: $$ 99^{\circ} + 0.5833^{\circ} = 99.5833^{\circ} $$ 3. Now, we need to calculate $$\sec(99.5833^{\circ})$$. The secant function is the reciprocal of the cosine function: $$ \sec(99.5833^{\circ}) = \frac{1}{\cos(99.5833^{\circ})} $$ 4. Using a calculator, find $$\cos(99.5833^{\circ})$$: $$ \cos(99.5833^{\circ}) \approx -0.1000 $$ 5. Now, calculate $$\sec(99.5833^{\circ})$$: $$ \sec(99.5833^{\circ}) = \frac{1}{-0.1000} \approx -10.0000 $$ Thus, the decimal approximation for $$\sec 99^{\circ} 35^{\prime}$$ is: $$ \sec 99^{\circ} 35^{\prime} \approx -10.0000 $$ So, the final answer is: $$ \boxed{-10.0000} $$

Use a calculator to find a decimal approximation for the following expression. \[ \sec 99^{\circ} 35^{\prime} \] \( \sec 99^{\circ} 35^{\prime}=\square \) (Type an integer or decimal rounded to four decimal places as needed.)

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Use a calculator to find a decimal approximation for the following expression. \[ \sec 99^{\circ} 35^{\prime} \] \( \sec 99^{\circ} 35^{\prime}=\square \) (Type an integer or decimal rounded to four decimal places as needed.)

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