Question

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

Explanation:

⚡ Using what you learned: Trigonometric Identities

Step 1: Identify the even-odd property of cosecant

The cosecant function is the reciprocal of the sine function:

$$ \csc(\theta) = \frac{1}{\sin(\theta)} $$

Since sine is an odd function, we have:

$$ \sin(-\theta) = -\sin(\theta) $$

Therefore, cosecant is also an odd function:

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

Step 2: Calculate the 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