SIN Full Form

Sin is a mathematics term used for “sine”. It is a trigonometric function. In the context of a right-angled triangle, the sine of an acute angle is defined as the ratio of the length of the side directly opposite the angle to the length of the longest side (hypotenuse) of the triangle.

Sin \Theta = \frac{p}{h}

The definitions of sine can be expanded more broadly to include any real value in terms of the lengths of certain line segments in a unit circle. Also, it can be extended to arbitrary positive and negative values as well as complex numbers according to more recent definitions that represent them as infinite series or as the solutions to certain differential equations.

Sine Function Value For Some Angles (In Degrees)

\sin 0 = 0 ,\\ \\

\sin 30 = \frac{1}{2} ,\\ \\

\sin 45 = \frac{1}{\sqrt{2}},\\ \\

\sin 60 = \frac{\sqrt{3}}{2}, \\ \\

\sin 90 = 1,\\ \\

\sin 120 = \frac{\sqrt{3}}{2} ,\\ \\

\sin 150 = \frac{1}{2} ,\\ \\

\sin 180 = 0 ,\\ \\

\sin 270 = -1 ,\\ \\

\sin 360 = 0

Sine Graph Function

Sine graph is also considered as the sine wave and is a type of continuous wave and smooth periodic function.

Graph of sine function y = sin(x) ,

Domain: (-\infty, \infty)

Range: [-1,1]or -1\leq y\leq 1

y intercept: (0,0)

x intercept: n \pi , where n is an integer.

Period: 2\pi

Continuity: Continuous on (-\infty, \infty)

Symmetry: origin (odd function)

Maximum Value: Occurs when x=\frac{\pi}{2}+2n\pi , when n is an integer.

Minimum Value: Occurs when x=\frac{3\pi}{2}+2n\pi , when n is an integer.

Other Trigonometric Functions

Other trigonometric functions in the context of a right-angled triangle are:

1. Cos Function :

Cos is the term used for cosine. Cos of an acute angle of the right-angled triangle is defined as the ratio of the length of the side on which the angle is drawn to the longest side (hypotenuse).

Cos \Theta = \frac{b}{h}

2. Tan Function :

Tan is the term used for the tangent. Tan of an acute angle of the right-angled triangle, is defined as the ratio of the length of the side directly opposite to the angle to the length of the side on which the angle is drawn.

Tan \Theta = \frac{p}{b}

3. Cosec Function:

Cosec is the term used for cosecant. The Cosec of an acute angle of the right-angled triangle is defined as the ratio of the longest side (hypotenuse) to the length of the side directly opposite to the angle.

Cosec \Theta = \frac{h}{p}

4. Sec Function

Sec is the term used for secant. Sec of an acute angle of the right-angled triangle is defined as the ratio of the longest side (hypotenuse) to the length of the side on which the angle is drawn.

Sec \Theta = \frac{h}{b}

5. Cot Function:

Cot is the term used for cotangent. The Cot of an acute angle of the right-angled triangle is defined as the ratio of the length of the side on which the angle is drawn to the length of the side directly opposite to the angle, i.e., the reciprocal of the tan function.

Cot \Theta = \frac{b}{p}