sec x= 1cos x,,x= 1sin x, x= cos xsin x, each with a nonzero denominator. The inverse trigonometric functions return a single principal angle. They are different from reciprocal ratios. **Function** | **Domain** | **Range** arcsin x | [-1,1] | [- 2, 2] arccos x | [-1,1] | [0,pi] arctan x | R | (- 2, 2) For example, arcsin(sin 5pi6)= 6, because the returned value must lie in the principal range. The graphs arise by reflecting appropriately restricted sine, cosine and tangent graphs in y=x.

\(\sec x=\dfrac1{\cos x},\quad\mathrm{cosec}\,x=\dfrac1{\sin x},\quad\cot x=\dfrac{\cos x}{\sin x}\), each with a nonzero denominator.

The inverse trigonometric functions return a single principal angle. They are different from reciprocal ratios.

For example, \(\arcsin(\sin\dfrac{5\pi}{6})=\dfrac\pi6\), because the returned value must lie in the principal range. The graphs arise by reflecting appropriately restricted sine, cosine and tangent graphs in \(y=x\).

Trigonometry

International Baccalaureate Mathematics: Analysis and Approaches Higher Level

Function	Domain	Range
\(\arcsin x\)	\([-1,1]\)	\(\left[-\dfrac\pi2,\dfrac\pi2\right]\)
\(\arccos x\)	\([-1,1]\)	\([0,\pi]\)
\(\arctan x\)	\(\mathbb R\)	\(\left(-\dfrac\pi2,\dfrac\pi2\right)\)

Inverse Trigonometric Functions (HL only)

Inverse Trigonometric Functions (HL only)