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 ...
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....
Thetypes of functionsare defined on the basis of the mapping, degree, and math concepts. The expression used to write the function is the prime defining factor for a function. Along with expression, the relationship between the elements of the domain set and the range set also accounts for t...
GraphsofTrigonometricFunctions PropertiesofSineandCosineFunctionsThegraphsofy=sinxandy=cosxhavesimilarproperties:1.Thedomainisthesetofrealnumbers.2.Therangeisthesetofyvaluessuchthat1y1.3.Themaximumvalueis1andtheminimumvalueis–1.4.Thegraphisasmoothcurve.5.Eachfunctioncyclesthroughallthevaluesofthe...
Use the results of part 1 above to express 5 of the trigonometric functions in terms of the cosine function only? Use the results of part 1 above to express 5 of the trigonometric functions in terms of sine function only? Answer More...
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 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...