Page 12 - 11-Math-11 Trigonometric Functions and their Graphs

111. .QTuriagdornaotmiceEtrqicuFautinocntsions and their Graphs eeLLeeaarrnn..PPuunnjjaabb

In a similar way, we can draw the graph for the interval from 0° to -360°. This will
complete the graph of y = cos x from -360° to 360° i.e. from - 2π to 2π , which is given below:

As in the case of sine graph, the cosine graph is also extended
on both sides of x-axis through an interval of 2Ï€ as shown above:

11.7 Graph of y = tan x from -π To π

We know that tan (-x) = - tan x and tan (Ï€ - x) = - tan x, so the values of tan x for
x = 0°, 30°, 45°, 60° can help us in making the table.

Also we know that tan x is undefined at x = ± 90°, when

i) x approaches π from left i.e., x → π - 0, tan x increases indefinitely in I Quard.
2 2

ii) x approaches π from right i.e., x → π + 0 , tan x increases indefinitely in IV Quard.
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iii) x approaches - π from left i.e., x→-π -0 tan x increases indefinitely in II Quard.
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version: 1.1

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