Calculating the Value of sin 30°: Using the Unit Circle and Special Triangle

sin 30°

To find the value of sin 30°, you can use the unit circle or the special triangle

To find the value of sin 30°, you can use the unit circle or the special triangle.

1. Using the unit circle:
On the unit circle, which is a circle with a radius of 1, the point (cos θ, sin θ) represents the angle θ. Since we want to find sin 30°, we need to locate the point on the unit circle that corresponds to an angle of 30°.

To do this, we draw the angle 30° in standard position (starting from the positive x-axis and rotating counterclockwise). The angle intersects the unit circle at the point where the terminal side of the angle intersects the circle.

If you draw this angle, you’ll see that the terminal side intersects the unit circle at the point (√3/2, 1/2). This means that sin 30° = 1/2.

2. Using the special triangle:
Another way to find the value of sin 30° is by using a special triangle known as the 30-60-90 triangle. In this triangle, the side opposite the 30° angle is half the hypotenuse.

The triangle has side lengths in the ratio 1:√3:2, where the side opposite the 30° angle is 1, the side opposite the 60° angle is √3, and the hypotenuse is 2.

Since sin is defined as the ratio of the opposite side to the hypotenuse, sin 30° is equal to 1/2.

Therefore, sin 30° = 1/2.

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