Page 16 - DMTH201_Basic Mathematics-1

Unit 1: Trigonometric Functions-I

Notes

As you would expect by now, the graph of the cosecant looks much like the graph of the secant.

1.3.4 Domain and Range of Trigonometric Functions

From the definition of sine and cosine functions, we observe that they are defined for all real
numbers. Further, we observe that for each real number x, – 1 ≤ sin x ≤ 1 and – 1 ≤ cos x ≤ 1
Thus, domain of y = sin x and y = cos x is the set of all real numbers and range is the interval [–1, 1],
i.e., −1 ≤ y ≤ 1. Range and domains of trigonometric function are given in a table shown below:

I quadrant II quadrant III quadrant IV quadrant
Sine increases from 0 decreases from decreases from increases from
to 1 1 to 0 0 to −1 −1 to 0
Cosine decreases from decreases from increases from increases from 0
1 to 0 0 to – 1 −1 to 0 to 1

Tan increases from 0 increases from increases from 0 increases from
to ∞ –∞ to 0 to ∞ −∞ to 0
Cot decreases from decreases from decreases from decreases from
∞ to 0 0 to −∞ ∞ to 0 0 to −∞
Sec increases from 1 increases from decreases from decreases from
to ∞ −∞ to −1 −1 to −∞ ∞ to 1
Cosec decreases from increases from 1 increases from decreases from
∞ to 1 to ∞ −∞ to −1 −1 to −∞

Task Find the cot and cosec values of triangle where, equals to 30, 60 and 45
degree.

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