Question

258 sin 179°× cos 179°/ sin 358°

Answer 1

В числителе пользуемся формулой синуса двойного угла, получаем

(129sin358)/sin358=129 и всё.

Answer 2

To evaluate the expression $258 \times \sin(179^\circ) \times \cos(179^\circ) / \sin(358^\circ)$, let's break it down step by step.

1. Calculate sin(179°): $\sin(179^\circ) \approx \sin(180^\circ - 1^\circ)$ $\sin(179^\circ) = \sin(1^\circ)$

   Note: $\sin(1^\circ)$ is approximately $0.017452$.

2. Calculate cos(179°): $\cos(179^\circ) \approx -\cos(180^\circ - 1^\circ)$ $\cos(179^\circ) = -\cos(1^\circ)$

   Note: $\cos(1^\circ)$ is approximately $0.999848$.

3. Calculate sin(358°): $\sin(358^\circ) \approx \sin(360^\circ - 2^\circ)$ $\sin(358^\circ) = \sin(2^\circ)$

   Note: $\sin(2^\circ)$ is approximately $0.034899$.

4. Substitute values and calculate:

   $$\frac{258 \times \sin(179^\circ) \times \cos(179^\circ)}{\sin(358^\circ)} = \frac{258 \times 0.017452 \times 0.999848}{0.034899}$$

Now, let's plug these values into a calculator to find the result. The result is approximately $258.001$.

Answer 3

Let's break down the expression step by step:

1. $\sin(179^\circ)$ is the sine of $179^\circ$.
2. $\cos(179^\circ)$ is the cosine of $179^\circ$.
3. $\sin(358^\circ)$ is the sine of $358^\circ$.

First, let's find the values of $\sin(179^\circ)$, $\cos(179^\circ)$, and $\sin(358^\circ)$:

1. $\sin(179^\circ)$: Using the fact that $\sin(\theta) = \sin(180^\circ - \theta)$, we have: $\sin(179^\circ) = \sin(180^\circ - 1^\circ) = \sin(1^\circ)$

The sine of $1^\circ$ is approximately $0.017452$ (rounded to 6 decimal places).

2. $\cos(179^\circ)$: Using the fact that $\cos(\theta) = -\cos(180^\circ - \theta)$, we have: $\cos(179^\circ) = -\cos(180^\circ - 1^\circ) = -\cos(1^\circ)$

The cosine of $1^\circ$ is approximately $0.999848$ (rounded to 6 decimal places).

3. $\sin(358^\circ)$: Using the fact that $\sin(\theta) = -\sin(360^\circ - \theta)$, we have: $\sin(358^\circ) = -\sin(360^\circ - 2^\circ) = -\sin(2^\circ)$

The sine of $2^\circ$ is approximately $0.034899$ (rounded to 6 decimal places).

Now, let's substitute these values into the original expression and calculate:

$\frac{\sin(179^\circ) \times \cos(179^\circ)}{\sin(358^\circ)} = \frac{0.017452 \times 0.999848}{0.034899}$

Now, let's calculate this expression:

$\frac{0.017452 \times 0.999848}{0.034899} \approx 0.499963$

So, $\frac{\sin(179^\circ) \times \cos(179^\circ)}{\sin(358^\circ)}$ is approximately $0.499963$ (rounded to 6 decimal places).