The period of a functionThe graph of y = sin xThe graph of y = cos xThe graph of y = sin axThe graph of y = tan xLET US BEGINwith some algebraic language. When we write "nπ," where n could be any integer, we mean "any multiple of π."0, ±π, ±2π, ±3π, . ....
A sine wave made by a circle:A sine wave produced naturally by a bouncing spring:Plot of SineThe Sine Function has this beautiful up-down curve (which repeats every 2π radians, or 360°).It starts at 0, heads up to 1 by π/2 radians (90°) and then heads down to −1....
Any function f ( x ) that has the property f ( x + p ) = f ( x ) is said to be periodic with a period p . If p is the smallest positive number for which this is true, p is called the period of f ( x ). Both the sine and the cosine functions have a characteristic ...
GraphsofTrigonometricFunctions PropertiesofSineandCosineFunctionsThegraphsofy=sinxandy=cosxhavesimilarproperties:1.Thedomainisthesetofrealnumbers.2.Therangeisthesetofyvaluessuchthat1y1.3.Themaximumvalueis1andtheminimumvalueis–1.4.Thegraphisasmoothcurve.5.Eachfunctioncyclesthroughallthevaluesofthe...
Learn the meaning of the amplitude of a function. Understand the method to find the amplitude of a sine function from the wave formula and graph...
The sine function forms a wave that starts from the origin. sin θ = 0 when θ = 0˚, 180˚, 360˚, … Maximum value of sin θ is 1 when θ = 90 ˚. Minimum value of sin θ is –1 when θ = 270 ˚. So, the range of values of sin θ is –1 ≤ sin θ≤ 1...
In the case of sine functions, the parent function is sin(x), and its period is 2 pi. How do you find the period of a sine wave? To find the period of a sine wave with equation f(x) = sin(Ax), use the formula Period = 2pi/|A|. If |A| = 1, then the period of the ...
The domain of a trigonometric function is the value of θ in Sinθ, and the range is the final numeric value of Sinθ. This concept can be similarly applied to all the other trigonometric functions. Further, the domain values can be any angular values, but here we have the principal valu...
The Sine Wave From the above graph, which shows the sine function from−3πto+5π, you can probably guess why the graph of the sine function is called the sine "wave": the circle's angles repeat themselves with every revolution of the unit circle, so the sine's values repeat themselv...
is often said toleadthe sine function (or the sine functionlagsthe cosine function). Both sine and cosine fall under the category of sinusoids, since the cosine graph is simply a 90º shift to the left of the sine graph. The sine and cosine functions are the most popular of the trigon...