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GRAPH OF tan x : y = tan x, x Î R, x ¹ (2n + 1) p/2, n Î I, y Î R

\The points (2n+1)p/2, n ÎI at which the value of tangent function approaches infinity and indefinite. When we draw the graph of tan x, a dashed line is drawn to show where the values of the tangent function is undefined. These lines are known as 'Asymptotes'.

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Fig. 17

Graphs of y = a sin (bx + c) and y = a cos(bx + c)

Before considering the graphs of (i) y = a sin(bx + c) and (ii) y = a cos(bx + c) we will consider the following graphs.

i) y = sin x   ii) y = 2 sin x   iii) 3 sin x

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i) Here the additional factor to sine function of x is 'a' i.e., y = a sin x, allows for amplitude vibration of the sine function. The amplitude |a| is the maximum deviation from the x-axis i.e. displacement along y-axis from the x-axis. This is half the difference between the maximum and minimum values of the graph (This is also true for cosine function).

Fig. 18


5. 1 Circular function
5. 2 Periodic function
5. 3 Even & Odd
5.4 Graphs of Trigonometric Functions Supplementary Problems

Chapter 6

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