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I have enjoyed my session with Aparna and it was helpful. I will hope to see her as my Math tutor in future sessions as well. Your tutor has been such an inspiration to me as I have difficulty getting some of the physics concepts down and truly understanding them. Thus, we now have. Hence, our range will now move to [1,5] We can adopt the same method for drawing the graphs of other trigonometric functions. But remember first you should convert the given functions of the form. The phase shift is the horizontal shift away from the standard graph of the trigonometric function.
If the phase shift is positive, there has been a horizontal shift to the right and if it is negative, there has been a horizontal shift to the left. In reading off the phase shift, make sure you have the function in the form above. Now we see the correct phase shift, is?
In the graph we can see graph of sin 2x -? We know trigonometric functions are periodic functions. Sinx and cos x are periodic functions with period 2? But tan and cot remain unchanged when x is increased by? So, they are periodic functions with period?. So, the period of cosine function is also 2? But for a tangent function. Change in its value changes horizontal stretching.
Also, the period is unchanged by vertical scaling or shifting or by horizontal shifting. We know basic trigonometric functions are sinx, cosx, tanx. These functions are periodic functions. The period is the shortest interval over which the function runs through one complete cycle of its graph.
Sinx and cos x are periodic functions with period 2?. But tan and cot remain unchanged when x is increased by pi. Amplitude See the graph of sinx. We know its range is [-1, 1]. The amplitude of the sine and cosine functions is half the vertical distance between its minimum value and its maximum value. The vertical shifts do alter the greatest and least values that the function attains but do not alter the amplitude.
The tangent function has no amplitude, because the tangent function has no minimum or maximum value. Another important formula is given below. We can use this formula when two sides and the included angle are given.
The area of triangle is given by. To know the the parameters refer here. Proof Let ABC be any of the triangles in the above figures. The study of Trigonometry was first started in India. The ancient Indian mathematicians Aryabhatta A. D , Bhaskara I A. D , Bhaskara A.
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