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Introduction:-
We need to know the period, phase, amplitude, maximum, and lowest turning points to create the trigonometry graphs of six trigonometric functions Sine, Cosine, Tangent, cosecant, secant, and cotangent. All of the trigonometric functions have graphs as well.
Trigonometric graphs:-
In trigonometric function graphs, the domain value is shown on the horizontal x-axis and the range value is shown on the vertical y-axis. The graphs of Sin and Tan pass through the origin, whereas the graphs of other trigonometric functions don’t pass.
[-1, 1] is a limited range of sin and cos.
Graph of all trigonometric functions:-
The following are the six trigonometric functions:
1. sine
2. cosine
3. tangent
4. cosecant
5. secant
6. cotangent
Trigonometric graphs for these Trigonometry functions are given below:-
1.sine function
The sine of an angle is a trigonometric function indicated by sin x, where x represents the angle. The sine function is the ratio of the perpendicular to the hypotenuse of a right-angled triangle.
Graph of the sine function:-
f(x)=sin(x)
[-1, 1] is the range.
2π is the period.
x= k π, where k is an integer, is the x-intercept.
y-intercepts: y = 0
The maximum points are (π/2 + 2 k π, 1), where k is an integer.
(3π/2 + 2 k π, -1) is the minimal point, where k is an integer.
Since sin(-x) = – sin (x), sin (x) is an odd function with a symmetric graph with respect to the origin (0 , 0).
Sin (x) increases over time and from 0 to 2π on the intervals (0, π/2) and (3π/2, 2π), and decreases on the interval (π/2, 3π/2).
2. Cosine function
One of the most important mathematical trigonometric ratios is cosine. The cosine function is the ratio of the lengths of the side adjacent to the angle and the hypotenuse of a right-angled triangle.
Graph of cosine function:-
The domain of cosine is real numbers.
[-1, 1] is the range.
2π is the period.
x = π/2 + k π, where k is an integer, is the x-intercept.
y-intercepts: y = 1
maximum points is (2 k π, 1), where k is an integer.
(π + 2 k π, -1) is the minimal point, where k is an integer.
Because cos(-x) = cos (x), cos (x) is an even function with asymmetric graph in relation to the y axis.
Cos (x) is decreasing on (0, π)and increasing on (π, 2π).
3.tangent function
The tangent function is defined as the ratio of the sine and cosine functions and The tangent function is defined as the ratio of the perpendicular to the base of the triangle is a right-angled triangle.
Graph of tangent function:-
All real numbers except (π/2 + k π), where k is an integer, are in the domain.
All real numbers are the range of this function.
π is the period.
(x = k pi )is a x intercept, k is an integer.
y = 0 ,is an y intercept.
Because tan(-x) = – tan(x), tan (x) is an odd function with a symmetric graph with respect to the origin.
tan (x) is increasing from – π/2 to π/2 over a period of time.
(x = π/2 + k π), where k is an integer, and is a vertical asymptote.
Cosecant function
The reciprocal of the trigonometric function sine is the cosecant function.
Graph of cosecant function:-
[-infinity, -1]U [1 + infinite] is the range of cosec function.
2π is the period cosecant graph.
Because Cosec(-x) = – cosec(x), cosec (x) is an odd function with a symmetric graph with respect to the origin.
Over one period, Cosec (x) decreases on (0, π/2) U (3π/2, 2π) and increases on (π/2, π) U (π /, 3π/2).
X = k π, where k is an integer, is a vertical asymptote.
Except for kπ, which is an integer, the domain includes all real numbers
Secant function
The reciprocal of the trigonometric function cosine is the secant function.
Graph of secant function:-
All real numbers except( π/2 + k π) are in the domain, and n is an integer.
[-infinity, -1]U [1 + infinite] is the range of secant function.
2 π is the period of the secant function.
Sec(-x) = sec (x)
sec (x) increases on (0, π/2) U (π/2, π) and decreases on (π, 3π/2) U (3π/2, 2π) during one period and from 0 to 2π.
x= (π/2 + k π), where k is an integer, is a vertical asymptote.
Cotangent function
The ratio of the adjacent to the opposing side is the cotangent of an angle in a right triangle. Generally represented by ‘cot’
Graph of cotangent function:-
Except for k π, which is an integer, the domain includes all real numbers.
All real numbers is the range of this function.
π is the period of cotangent function.
(x = π /2 + k π ) is x intercept where k is an integer.
cot(-x) = – cot(x), cot (x) is an odd function with a symmetric graph with respect to the origin.
cot (x) decreases through time and from 0 to pi.
X = k π, where k is an integer, is a vertical asymptote.
Conclusion:-
In trigonometry, there are six functions of an angle that are often applied. Sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant(cosec) are their names. All of the trigonometric functions have graphs as well.
In trigonometric function graphs, the domain value is shown on the horizontal x-axis and the range value is shown on the vertical y-axis.
