Inverse Trigonometric Functions
Inverse trigonometric functions invert the trigonometric functions on restricted domains, giving principal values in fixed ranges.
What is Inverse Trigonometric Functions?
Inverse trigonometric functions invert the trigonometric functions on restricted domains, giving principal values in fixed ranges.
Key formula / rule: The principal range of arcsin is [-π/2, π/2] and of arccos is [0, π].
Key points
- Identify the principal value branch of an inverse trigonometric function.
- Apply inverse trigonometric identities with their validity conditions.
Common exam trap
Applying the addition formula for arctan without the xy < 1 condition.
Definitions
- Term
Inverse Trigonometric Functions
- Meaning
Inverse trigonometric functions invert the trigonometric functions on restricted domains, giving principal values in fixed ranges.
- Term
Inverse Trigonometric Functions — explanation
- Meaning
The restriction of domain is what makes the inverse a function at all, so every identity involving inverses carries a range condition. Ignoring that condition is the standard source of wrong signs.
Learning objectives
Identify the principal value branch of an inverse trigonometric function.
Apply inverse trigonometric identities with their validity conditions.
Formulae
- Key point
The principal range of arcsin is [-π/2, π/2] and of arccos is [0, π].
- Key point
arctan x + arctan y = arctan((x+y)/(1-xy)) only when xy < 1.
- Key point
sin(arcsin x) = x for x in [-1, 1] but arcsin(sin t) = t only in the principal range.
Prerequisites
MAT-U5-TR-T1-S1-C2
Common mistakes
Applying the addition formula for arctan without the xy < 1 condition.
Assuming arcsin(sin t) equals t for every real t.
Keywords
Inverse
Trigonometric
Functions
Practice preview
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