Question: What Is The Sine Function Equation?

Why Sine is called sine?

In mathematics, the sine is a trigonometric function of an angle.

The word “sine” (Latin “sinus”) comes from a Latin mistranslation by Robert of Chester of the Arabic jiba, which is a transliteration of the Sanskrit word for half the chord, jya-ardha..

Why do we use sine?

The sine function is defined as the ratio of the side of the triangle opposite the angle divided by the hypotenuse. This ratio can be used to solve problems involving distance or height, or if you need to know an angle measure. Example: … To find the length of the side opposite the angle, d, we use the sine function.

What is sin equal to?

Always, always, the sine of an angle is equal to the opposite side divided by the hypotenuse (opp/hyp in the diagram). The cosine is equal to the adjacent side divided by the hypotenuse (adj/hyp). (1) Memorize: sine = (opposite side) / hypotenuse. cosine = (adjacent side) / hypotenuse.

How do you find the sine of a function?

Sin, Cos and TanThe sine of the angle = the length of the opposite side. the length of the hypotenuse.The cosine of the angle = the length of the adjacent side. the length of the hypotenuse.The tangent of the angle = the length of the opposite side. the length of the adjacent side.

What does a represent in a sine function?

The value A (in front of sin or cos) affects the amplitude (height). The amplitude (half the distance between the maximum and minimum values of the function) will be |A|, since distance is always positive. Increasing or decreasing the value of A will vertically stretch or shrink the graph.

What does a sine curve look like?

The domain of the sine function As you drag the point A around notice that after a full rotation about B, the graph shape repeats. The shape of the sine curve is the same for each full rotation of the angle and so the function is called ‘periodic’. The period of the function is 360° or 2π radians.

Who invented sine?

Hipparchus of NicaeaThe first trigonometric table was apparently compiled by Hipparchus of Nicaea (180 – 125 BCE), who is now consequently known as “the father of trigonometry.” Hipparchus was the first to tabulate the corresponding values of arc and chord for a series of angles.

How do you find the maximum and minimum of a sine function?

Graphs: Sine and CosineThe additional term A in the function y = A + sin x allows for a vertical shift in the graph of the sine functions. … The additional factor B in the function y = B sin x allows for amplitude variation of the sine function. … The maximum value is 1 + 2 = 3. … The maximum value is 4 + 3 = 7.More items…

What is the period of sin?

2πThe period of the sine curve is the length of one cycle of the curve. The natural period of the sine curve is 2π. So, a coefficient of b=1 is equivalent to a period of 2π. To get the period of the sine curve for any coefficient b, just divide 2π by the coefficient b to get the new period of the curve.

What is C in a sine function?

The value of variable ‘c’ moves the sine graph to the right or the left. When c > 0, the graph moves to the left. When c < 0, the graph moves to the right. This horizontal movement is called the phase shift. The phase shift appears to be equal to the value of '–c'.

What is the equation for a sinusoidal function?

If you are given the equation y = A sin(kx + c) + d, then the phase shift equals -c/k. The calculation is identical if you replace the sin with cos.