Sin 390 Without Calculator

How to Calculate sin(390)

To find sin(390) without a calculator, follow these steps:

1. Understand that 390 degrees is more than 360 degrees, so we'll use the concept of coterminal angles.
2. Find the reference angle by subtracting 360 degrees from 390 degrees.
3. Determine the sine value using the reference angle and the unit circle.

The sine of an angle is equal to the y-coordinate of the corresponding point on the unit circle.

Step-by-Step Calculation

Step 1: Find the Coterminal Angle

Since 390° is greater than 360°, we can find its coterminal angle by subtracting 360°:

So, 390° is coterminal with 30°.

Step 2: Determine the Sine Value

Now, we can find sin(30°) using the unit circle:

Since sine is positive in the first quadrant where 30° lies, the sine of 390° is the same as the sine of 30°.

Final Result

The sine of 390 degrees is equal to the sine of 30 degrees, which is 0.5.

Worked Example

Let's calculate sin(390°) step by step:

1. Subtract 360° from 390°: 390° - 360° = 30°
2. Find sin(30°): 0.5
3. Therefore, sin(390°) = sin(30°) = 0.5

This shows that sin(390°) is equal to 0.5.

Formula Used

This formula is based on the unit circle definition of sine, where the sine of an angle is equal to the y-coordinate of the corresponding point on the unit circle.