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....
different methods can be used to draw the graph of a trigonometric function. the detailed explanation of one of the efficient methods is given below. while drawing a graph of the sine function, convert the given function to the general form as a sin (bx – c) + d in order to find ...
GraphsofTrigonometricFunctions PropertiesofSineandCosineFunctionsThegraphsofy=sinxandy=cosxhavesimilarproperties:1.Thedomainisthesetofrealnumbers.2.Therangeisthesetofyvaluessuchthat1y1.3.Themaximumvalueis1andtheminimumvalueis–1.4.Thegraphisasmoothcurve.5.Eachfunctioncyclesthroughallthevaluesofthe...
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 ...
From the above graph, which shows the sine function from −3π to +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 themselves with ...
Now you will graph the sine function on page 1.14 a. Create a scatter plot in s2 on page 1.14 What variables do you need to use for the x-values and y-values? b. Graph y = sin(x) in f2(x). How does the shape of the graph differ from the cosine function? 7. S ketch the ...
The six basic trigonometric functions are sine function, cosine function, secant function, co-secant function, tangent function, and co-tangent function. The trigonometric functions and identities are the ratio of sides of a right-angled triangle. The sides of a right triangle are the perpendicular...
The graphs of tanxtanx, cotxcotx, secxsecx and cscxcscx are not as common as the sine and cosine curves that we met earlier in this chapter. However, they do occur in engineering and science problems. They are interesting curves because they have discontinuities. For ...
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...