QuestionJuly 16, 2025

Use the trigonometric function values of the quadrantal angles to evaluate. 4cot270^circ +3csc270^circ 4cot270^circ +3csc270^circ =square (Simplify your answer. Type an integer or a fraction.)

Use the trigonometric function values of the quadrantal angles to evaluate. 4cot270^circ +3csc270^circ 4cot270^circ +3csc270^circ =square (Simplify your answer. Type an integer or a fraction.)
Use the trigonometric function values of the quadrantal angles to evaluate. 4cot270^circ +3csc270^circ 4cot270^circ +3csc270^circ =square (Simplify your answer. Type an integer or a fraction.)

Solution
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Answer

Undefined Explanation 1. Evaluate cot(270^{\circ}) The cotangent of 270^{\circ} is undefined because \tan(270^{\circ}) = \frac{\sin(270^{\circ})}{\cos(270^{\circ})} = \frac{-1}{0}, leading to division by zero. 2. Evaluate csc(270^{\circ}) The cosecant of 270^{\circ} is -1 because csc(270^{\circ}) = \frac{1}{\sin(270^{\circ})} = \frac{1}{-1} = -1. 3. Simplify the expression Since cot(270^{\circ}) is undefined, the entire expression 4 \cdot cot(270^{\circ}) + 3 \cdot csc(270^{\circ}) is undefined.

Explanation

1. Evaluate $cot(270^{\circ})$<br /> The cotangent of $270^{\circ}$ is undefined because $\tan(270^{\circ}) = \frac{\sin(270^{\circ})}{\cos(270^{\circ})} = \frac{-1}{0}$, leading to division by zero.<br /><br />2. Evaluate $csc(270^{\circ})$<br /> The cosecant of $270^{\circ}$ is $-1$ because $csc(270^{\circ}) = \frac{1}{\sin(270^{\circ})} = \frac{1}{-1} = -1$.<br /><br />3. Simplify the expression<br /> Since $cot(270^{\circ})$ is undefined, the entire expression $4 \cdot cot(270^{\circ}) + 3 \cdot csc(270^{\circ})$ is undefined.
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