CBSE NOTES CLASS 12 MATHEMATICS CHAPTER 2

INVERSE TRIGONMETRIC FUNCTIONS

Domains and Ranges of Different Trigonometric Functions

 Function Domain Range sin R [– 1, 1] cos R [– 1, 1] tan R cot R – { x : x = nπ, n ∈ Z} R sec R – (-1,1) cosec R – { x : x = nπ, n ∈ Z} R – (-1,1)

Inverse Trigonometric Functions and Domains Principal Range

 Functions Domain Range (Principal value branches) y = sin–1 x [–1,1] $\left[–\frac{\mathrm{\pi }}{2},\frac{\mathrm{\pi }}{2}\right]$ y = cos–1 x [–1,1] [0,π] y = cosec–1 x R– (–1,1) y = sec–1 x R– (–1,1) $\left[0,\mathrm{\pi }\right]–\left\{\frac{\mathrm{\pi }}{2}\right\}$ y = tan–1 x R $\left(–\frac{\mathrm{\pi }}{2},\frac{\mathrm{\pi }}{2}\right)$ y =cot-1 x R (0, π)

Graphs of Different Trigonometric Functions and Inverse Trigonometric Functions

• The graph of the function y = sin–1 x can be obtained from the graph of y = sin x by interchanging x and y axes.

• The graph of an inverse function can be obtained from the corresponding graph of original function as a mirror image (i.e., reflection) along the line y = x.

Properties of Inverse Trigonometric Functions

1. (i)

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2. (i)

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3. (i)

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4. (i)

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5. (i)

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6. (i)

(ii)

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