How to find the value of sin 480 degree
To find the value of sin 480 degrees, we need to understand a few things about the sine function and the unit circle.
1. The sine function represents the ratio of the length of the side opposite an angle in a right triangle to the hypotenuse of the triangle.
2. The unit circle is a circle with a radius of 1 unit, centered at the origin of a coordinate plane. It is useful to visualize angles and trigonometric functions.
To find the value of sin 480 degrees, we can use the concept of periodicity of the sine function. The sine function has a period of 360 degrees or 2π radians. This means that the value of sin x is the same as sin (x ± 360°), where ± is any integer.
The angle 480 degrees can be rewritten as 480 - 360 = 120 degrees. The sine of 480 degrees is equivalent to the sine of 120 degrees.
Now let's find the value of sin 120 degrees.
1. Draw a unit circle and mark the angle of 120 degrees.
2. From the center of the unit circle, draw a line that intersects the circle and forms the angle of 120 degrees with the positive x-axis.
3. The vertical component of the point where the line intersects the circle represents the sine of the angle.
4. Use the Pythagorean theorem to find the length of the vertical component (opposite side) and divide it by the hypotenuse (radius of the unit circle which is 1) to find the sine.
For a 120-degree angle, you can see that the vertical component is √3/2 and the hypotenuse is 1. Therefore, sin 120 degrees = (√3/2) / 1 = √3/2.
So, the value of sin 480 degrees is √3/2.
subtract full circles (360º), until the angle value is less than 360º
in this case , 120º ... 60º reference angle in Quad II