What is the value of sin (1920) ?

Options

A. `1//2`
B. `(1)/(sqrt(2))`
C. `(sqrt(3))/(2)`
D. `1//3`

Explanation

To find the value of sin(1920°), we can follow these steps:

### Step 1: Reduce the angle
First, we need to reduce the angle 1920° to an equivalent angle within the range of 0° to 360°. We can do this by subtracting multiples of 360°.

\[ 1920 \div 360 = 5.3333 \quad \text{(approximately)} \]

This means that 1920° is equivalent to \(5 \times 360° + \text{remainder}\).

Calculating \(5 \times 360°\):

\[ 5 \times 360° = 1800° \]

Now, subtract this from 1920°:

\[ 1920° - 1800° = 120° \]

So, \(1920° \equiv 120° \mod 360°\).

### Step 2: Determine the quadrant
The angle 120° is in the second quadrant (90° to 180°).

### Step 3: Use the sine function
In the second quadrant, the sine function is positive. We can find the sine of 120° using the reference angle.

The reference angle for 120° is:

\[ 180° - 120° = 60° \]

### Step 4: Find the sine value
Now, we can find the sine of 120°:

\[ \sin(120°) = \sin(60°) \]

From trigonometric values, we know:

\[ \sin(60°) = \frac{\sqrt{3}}{2} \]

Thus,

\[ \sin(120°) = \frac{\sqrt{3}}{2} \]

### Conclusion
Therefore, the value of \(\sin(1920°)\) is:

\[ \sin(1920°) = \frac{\sqrt{3}}{2} \]

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