Question

if \\(\csc 60^{\circ} = 1.155\\), what is \\(\csc(-60^{\circ})\\)?

Explanation:

⚡ Using what you learned: Trigonometric Identities

Step 1: Apply the odd-even identity for cosecant

The cosecant function is an odd function, which means:

$$ \csc(-\theta) = -\csc(\theta) $$

Step 2: Substitute the given value

Substitute \( \theta = 60^\circ \) into the identity:

$$ \csc(-60^\circ) = -\csc(60^\circ) $$

Given that \( \csc 60^\circ = 1.155 \):

$$ \csc(-60^\circ) = -1.155 $$

Answer:

-1.155