QuestionJune 18, 2025

Use the trigonometric function values of the quadrantal angles to evaluate. 3cot90^circ -4csc270^circ 3cot90^circ -4csc270^circ =square (Simplify your answer.Type an integer or a fraction.)

Use the trigonometric function values of the quadrantal angles to evaluate. 3cot90^circ -4csc270^circ 3cot90^circ -4csc270^circ =square (Simplify your answer.Type an integer or a fraction.)
Use the trigonometric function values of the quadrantal
angles to evaluate.
3cot90^circ -4csc270^circ 
3cot90^circ -4csc270^circ =square 
(Simplify your answer.Type an integer or a fraction.)

Solution
3.1(304 votes)

Answer

Undefined Explanation 1. Evaluate cot90^{\circ} cot90^{\circ} is undefined because cot\theta = \frac{1}{tan\theta} and tan90^{\circ} is undefined. 2. Evaluate csc270^{\circ} csc270^{\circ} = \frac{1}{sin270^{\circ}} = \frac{1}{-1} = -1. 3. Simplify the expression Substitute the values: 3 \cdot \text{undefined} - 4 \cdot (-1). The term 3 \cdot \text{undefined} makes the entire expression undefined.

Explanation

1. Evaluate $cot90^{\circ}$<br /> $cot90^{\circ}$ is undefined because $cot\theta = \frac{1}{tan\theta}$ and $tan90^{\circ}$ is undefined.<br />2. Evaluate $csc270^{\circ}$<br /> $csc270^{\circ} = \frac{1}{sin270^{\circ}} = \frac{1}{-1} = -1$.<br />3. Simplify the expression<br /> Substitute the values: $3 \cdot \text{undefined} - 4 \cdot (-1)$. The term $3 \cdot \text{undefined}$ makes the entire expression undefined.
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