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What is the similarities between a sine graph and a cosine graph?
Both sine and cosine graphs are periodic functions with a periodicity of (2\pi), meaning they repeat their values every (2\pi) radians. They both have an amplitude of 1, oscillating between -1 and 1. Additionally, the sine graph is a horizontal shift of the cosine graph; specifically, the cosine graph can be expressed as the sine graph shifted to the left by (\frac{\pi}{2}) radians. Both graphs exhibit similar shapes, featuring smooth, continuous waves.
What does the period of a trigonometric function represent?
The period of a trigonometric function represents the length of one complete cycle of the function's values before they start to repeat. For example, the sine and cosine functions both have a period of (2\pi), meaning their values repeat every (2\pi) radians. The period is crucial for understanding the function's behavior, frequency, and how it relates to real-world phenomena, such as sound waves and circular motion.
What jobs use trigonometry functions?
Often people involved in industrial production will use polar graphs to program their machines; take, for, example, a pretzel-making machine. They can graph the path the "dough-shaping" machine must follow on a polar graph.
What is the graph of f(t)(sin t cos t?
The graph of the function ( f(t) = \sin(t) \cos(t) ) can be simplified using the double-angle identity for sine, resulting in ( f(t) = \frac{1}{2} \sin(2t) ). This function oscillates between -0.5 and 0.5, with a period of ( \pi ). The graph will exhibit a wave-like pattern, with peaks and troughs occurring at intervals of ( \frac{\pi}{2} ). Overall, it is a smooth, continuous curve that represents the amplitude-modulated sine wave.
Sketch a Tangent Functions?
A tangent function is a trigonometric function that describes the ratio of the side opposite a given angle in a right triangle to the side adjacent to that angle. In other words, it describes the slope of a line tangent to a point on a unit circle. The graph of a tangent function is a periodic wave that oscillates between positive and negative values. To sketch a tangent function, we can start by plotting points on a coordinate plane. The x-axis represents the angle in radians, and the y-axis represents the value of the tangent function. The period of the function is 2π radians, so we can plot points every 2π units on the x-axis. The graph of the tangent function is asymptotic to the x-axis. It oscillates between positive and negative values, crossing the x-axis at π/2 and 3π/2 radians. The graph reaches its maximum value of 1 at π/4 and 7π/4 radians, and its minimum value of -1 at 3π/4 and 5π/4 radians. In summary, the graph of the tangent function is a wave that oscillates between positive and negative values, crossing the x-axis at π/2 and 3π/2 radians, with a period of 2π radians.
The length of one complete repetition of the cycle is called the what of the graph?
The length of one complete repetition of the cycle in a graph is called the period. In the context of periodic functions, the period is the distance along the x-axis after which the function's values repeat. For example, in trigonometric functions like sine and cosine, the period is typically (2\pi).
Property common to all trigonometric functions?
Trigonometric functions are periodic - they repeat after a period of pi, or 2 x pi.Trigonometric functions are periodic - they repeat after a period of pi, or 2 x pi.Trigonometric functions are periodic - they repeat after a period of pi, or 2 x pi.Trigonometric functions are periodic - they repeat after a period of pi, or 2 x pi.
What is period as it pertains to the graph of sine and cosine?
Period is how long it takes for the sine and cosine functions to restart repeating themselves. Both have a period of 2pi (360 degrees).
identity linear and nonlinear functions from graph?
identity linear and nonlinear functions from graph
How do you graph trigonometric functions with a degree in the parenthese?
Look on a unit circle graph and see what kind of pi it has. For example 90 degrees is pi/2
How do you graph cosine functions?
it is the same as a sin function only shifted to the left pi/2 units
How do you graph a quadratic functions?
Calculator
How do you graph cost revenue and profit functions?
There are a couple of graphs you could use. A pie graph or a bar graph.
Which of the functions below could have created this graph?
To accurately identify which function could have created the graph, I would need to see the specific graph in question. However, common functions that often produce recognizable graphs include linear functions (straight lines), quadratic functions (parabolas), exponential functions (curved growth), and trigonometric functions (sine, cosine waves). If you provide details about the graph's shape or key features, I can help narrow down the possible functions.
Can the graph of a functions be verticle line?
Yes the graph of a function can be a vertical or a horizontal line
What are the four functions of a graph?
it is like what you do on a map
Which functions have period 2 pi?
Sin cos sec cosec
