sinx
cosx
The trigonometric function sinx represents the sine of an angle. The sine of an angle in a right-angled triangle is defined as the ratio of the length of the side opposite to the angle and the length of the hypotenuse, which is the longest side of the triangle and opposite to the right angle.
However, when dealing with the sine of an angle in a broader sense, such as in calculus or trigonometry, we use the unit circle to define the sine function. The unit circle is a circle with a radius equal to 1 unit, and we represent an angle (in radians) as a point on the circle, where the angle is measured in the counterclockwise direction from the positive x-axis.
To find the sine of an angle in this context, we draw a perpendicular line from the point on the unit circle to the x-axis, which creates a right-angled triangle. The sine function is defined as the y-coordinate of the point where the perpendicular line intersects the circle.
Therefore, if we have an angle x, the sine of x (sinx) is equal to the y-coordinate of the point that represents x on the unit circle. We can use the values of sine for various angles to calculate and analyze waves, sound, and many other phenomena in physics and engineering.
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