NSW Y11 Maths - Extension 1 Inverse Trig Functions and Identities Inverse Trig Functions

NSW Syllabus Reference

NSW Syllabus Reference: ME-T1 Inverse Trigonometric Functions. This will require student to 

• define and use the inverse trigonometric functions (ACMSM119)
• sketch graphs of the inverse trigonometric functions
• use the relationships \(\sin(\sin ^{-1}x)=x\) and \(\sin^{-1}(\sin x) =x\), \(\cos(\cos ^{-1}x)=x\) and \(\cos^{-1}(\cos x) =x\), \(\tan(\tan ^{-1}x)=x\) and \(\tan^{-1}(\tan x) =x\) where appropriate, and state the values of \(x\) for which these relationships are valid
• prove and use the properties: \(\sin^{-1}(-x)=-\sin^{-1}x,\, \cos^{-1}(-x)=\pi -\cos^{-1}x,\, \tan^{-1}(-x)=- \tan ^{-1}x\) and \(\cos^{-1}x+ \sin^{-1}x=\dfrac{\pi}{2}\)
• solve problems involving inverse trigonometric functions in a variety of abstract and practical situations

Ref: https://educationstandards.nsw.edu.au/