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If \( \csc 60^{\circ}=1.155 \) what is \( \csc \left(-60^{\circ}\right) ? \)

Ask by Munoz Valdez. in the United States
Mar 11,2025

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Answer

\( \csc(-60^{\circ}) = -1.155 \)

Solution

To find \( \csc \left(-60^{\circ}\right) \), we can use the property of the cosecant function related to negative angles. The cosecant function is defined as: \[ \csc(-\theta) = -\csc(\theta) \] Applying this property, we have: \[ \csc(-60^{\circ}) = -\csc(60^{\circ}) \] Given that \( \csc(60^{\circ}) = 1.155 \), we can substitute this value into the equation: \[ \csc(-60^{\circ}) = -1.155 \] Thus, the value of \( \csc(-60^{\circ}) \) is: \[ \csc(-60^{\circ}) = -1.155 \]

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The cosecant function, \( \csc \), is an odd function, meaning that \( \csc(-x) = -\csc(x) \). So, in this case: \[ \csc(-60^\circ) = -\csc(60^\circ) \] Since \( \csc(60^\circ) = 1.155 \), we can substitute this value in: \[ \csc(-60^\circ) = -1.155 \] Therefore, \( \csc(-60^\circ) = -1.155 \).

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