Sin 300 cos 145 ctg 24

To evaluate the expression \( \sin 300^\circ \cdot \cos 145^\circ \cdot \cot 24^\circ \), we first need to find the values of each trigonometric function.

1. Find \( \sin 300^\circ \): \[ 300^\circ = 360^\circ - 60^\circ \implies \sin 300^\circ = -\sin 60^\circ = -\frac{\sqrt{3}}{2} \]

2. Find \( \cos 145^\circ \): \[ 145^\circ = 180^\circ - 35^\circ \implies \cos 145^\circ = -\cos 35^\circ \]

3. Find \( \cot 24^\circ \): \[ \cot 24^\circ = \frac{1}{\tan 24^\circ} \]

Now, substituting these values into the expression, we get:

\[ \sin 300^\circ \cdot \cos 145^\circ \cdot \cot 24^\circ = \left(-\frac{\sqrt{3}}{2}\right) \cdot \left(-\cos 35^\circ\right) \cdot \cot 24^\circ \]

This simplifies to:

\[ = \frac{\sqrt{3}}{2} \cdot \cos 35^\circ \cdot \cot 24^\circ \]

To complete the evaluation, we would need numerical values for \( \cos 35^\circ \) and \( \cot 24^\circ \).

Using a calculator,

• \( \cos 35^\circ \approx 0.8192 \)
• \( \cot 24^\circ \approx 2.4947 \)

Now, plug in these values:

\[ = \frac{\sqrt{3}}{2} \cdot 0.8192 \cdot 2.4947 \]

Calculating it step by step:

1. Calculate \( \frac{\sqrt{3}}{2} \): \[ \frac{\sqrt{3}}{2} \approx 0.8660 \]

2. Now calculate the product: \[ 0.8660 \cdot 0.8192 \cdot 2.4947 \approx 1.7614 \]

So, the final result is approximately \( 1.7614 \).

Thus,

\[ \sin 300^\circ \cdot \cos 145^\circ \cdot \cot 24^\circ \approx 1.7614 \]