Family Overview

In Plain Language

Topic 3.9 is about inverse trigonometric functions: arcsin, arccos, and arctan.

• Idea: input and output swap from the forward trig functions; inverse output is usually an angle (3.9.A.1).
• Notation: arcsin, arccos, arctan (also sin^-1, cos^-1, tan^-1) (3.9.A.2).
• Restriction: sine, cosine, and tangent must be restricted to one branch before they can be inverted (3.9.A.3).

Why It Matters

Inverse trig is how students recover angles from ratios—essential for triangles, slopes, and later equation solving (3.10).

How Families Can Help

• Ask: "Is this input allowed for arcsin or arccos?"
• Compare ranges: arcsin vs arccos vs arctan.
• Check calculator angle mode before interpreting an answer.

What Not to Do

• Do not use arcsin/arccos outside [-1, 1].
• Do not ignore range when adjusting arcsin(sin x).
• Do not assume any angle works for every inverse.