Topic explanation

Standard explanation

sin(arcsin x)=x on [-1,1], but arcsin(sin x)=x only inside the principal interval.

Key points

• Inverse identities
• rule
• worked example
• Inverse identities: sin(arcsin x)=x on [-1,1], but arcsin(sin x)=x only inside the principal interval.
• CONCEPT AND RULE: sin(arcsin x)=x on [-1,1], but arcsin(sin x)=x only inside the principal interval.
• METHOD: For inverse identities, identify the given information and required result. Select the matching defi
• sin(arcsin x)=x on [-1,1], but arcsin(sin x)=x only inside the principal interval.
• Worked pattern: arcsin(sin(5pi/6))=pi/6.

Labelled diagram