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mathuravasant
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State the domain and range for one cycle of y=cos(3(x - 45°)) +2 Show your work.
Please show us what you have tried and exactly where you are stuck.mathuravasant said:State the domain and range for one cycle of y=cos(3(x - 45°)) +2 Show your work.
You are having a great deal of trouble with these. I suspect the biggest cause isn't in the problems but in the definitions. I would suggest having a 3 x 5 card (or some other modern equivalent) stating what the domain, range, frequency, wave number, horizontal shift (or phase), and vertical shift are for each.mathuravasant said:like how do you find domain and range off from that given equation I just don't know what to do
A sinusoidal function is a mathematical function that describes a periodic oscillation, such as a wave or vibration. It is represented by the equation f(x) = A sin (Bx + C) + D, where A is the amplitude, B is the frequency, C is the phase shift, and D is the vertical shift.
A cosine function is a type of sinusoidal function that has a phase shift of 0 degrees, meaning it starts at the maximum value. A general sinusoidal function can have any phase shift, which will affect the starting point of the function. Additionally, the graphs of these functions differ slightly in shape, with the cosine function being slightly shifted to the left.
The period of a sinusoidal function is the length of one complete cycle of the function. It can be calculated by dividing 2π by the coefficient of x in the equation, or by finding the distance between two consecutive maximum or minimum points on the graph.
Sinusoidal functions are closely related to trigonometric ratios, specifically the sine and cosine functions. The sine function represents the vertical displacement of a point on a unit circle, while the cosine function represents the horizontal displacement. These functions can be used to model sinusoidal functions and vice versa.
Sinusoidal functions have many real-life applications, such as modeling sound waves, ocean tides, and electromagnetic waves. They are also used in fields such as engineering, physics, and music to analyze and predict the behavior of periodic phenomena.