Sin 1, or more precisely sin(1) where the 1 represents an angle in radians, is called the sine of 1 radian. It's a trigonometric function where the input is an angle, and the output is a ratio derived from the unit circle. This output ratio represents the y-coordinate of a point on the unit circle at the angle of 1 radian.
Understanding the Sine Function
- The sine function, often written as sin(x), is a fundamental concept in trigonometry.
- It relates an angle of a right triangle to the ratio of the opposite side to the hypotenuse.
- In the unit circle context, sin(x) is the y-coordinate of a point on the circle, with x as the angle from the positive x-axis.
The Meaning of sin 1
- When we say sin 1, we're using radians as the angle's unit.
- One radian is the angle subtended at the center of a circle by an arc whose length is equal to the radius of the circle.
- Therefore, sin 1 represents the sine of 1 radian.
- The value of sin(1) is approximately 0.84147, this is a unitless ratio.
Inverse Sine Function
It is important to distinguish this from the inverse sine function (also known as arcsin or sin-1), mentioned in the reference.
| Function | Input | Output | Description |
|---|---|---|---|
| sin(x) | Angle | Ratio | Returns the ratio of the opposite side to the hypotenuse for angle x. Or the y-coordinate of a point on the unit circle at angle x. |
| sin-1(y) | Ratio | Angle | Returns the angle whose sine is the ratio y. |
- The reference indicates that the inverse sine function or Sin-1 takes the ratio, Opposite Side / Hypotenuse Side and produces angle θ.
- It's also written as arcsin.
- For example, if sin(θ) = 0.5, then sin-1(0.5) = θ, which is 30 degrees or π/6 radians.
- sin 1 is not an inverse sine function; it is the basic sine of an angle, 1 radian.
In Conclusion
- sin 1 is not an inverse function.
- sin 1 is the sine of an angle (1 radian) resulting in a ratio.
- The inverse sine function will take a ratio as an input and output an angle.
