The sine of $\pi / 4$ is one of the most commonly encountered mathematics concepts in many college and university mathematics courses. It is known to be the ratio of the opposite side to the hypotenuse in a right triangle, and can be expressed as a trigonometric identity.
Trigonometric identity
The sine of an angle is equal to the ratio of the opposite side to the hypotenuse for any given right triangle. This ratio is then expressed as a trigonometric identity, and can be expressed as the following equation:
$$ \sin{\theta} = \frac{opposite}{hypotenuse} $$
Therefore, the sine of $\pi/4$ can be expressed as follows:
$$ \sin{(\pi/4)} = \frac{opposite}{hypotenuse} $$
Finding the Sine of $\pi/4$
Given that the sine of an angle is equal to the ratio of the opposite side to the hypotenuse of a right triangle, the sine of $\pi / 4$ can be found by finding the ratio of the opposite side to the hypotenuse. To do this, you need to first draw a right triangle with an angle of $\pi/4$.
The hypotenuse of the triangle is its long side, and in this case, the length of the long side is 1. The opposite side can be considered the side opposite to the angle of $\pi/4$.
The opposite side of the right triangle is 0.707, so the ratio of the opposite side to the hypotenuse of the triangle is 0.707. Therefore, the sine of $\pi / 4$ is equal to 0.707.
FAQ
What is the sine of $\pi/4$?
The sine of $\pi/4$ is equal to 0.707. It is known that the sine of an angle is the ratio of the opposite side to the hypotenuse for any given right triangle.
What is the value of $\sin^{-1}(0.707)$?
The value of $\sin^{-1}(0.707)$ is equal to $\frac{\pi}{4}$. Since the inverse sine is equal to the angle for which the sine is equal to the given value, $\sin^{-1}(0.707)$ means that the angle is $\frac{\pi}{4}$.
How can I find the sine of any angle?
You can find the sine of any angle by drawing a right triangle with the given angle. The sine of an angle is equal to the ratio of the opposite side to the hypotenuse of the triangle.
What is the ratio of the opposite side to the hypotenuse of the right triangle with an angle of $\pi/4$?
The ratio of the opposite side to the hypotenuse of the right triangle with an angle of $\pi/4$ is equal to 0.707.
What is the sine of an angle equal to?
The sine of an angle is equal to the ratio of the opposite side to the hypotenuse for any given right triangle.