2.4 Miscellaneous Examples

Screen Readable NCERT Class 12 Mathematics Textbook for Blind and Visually Impaired Students prepared by Professor T K Bansal.

Example 6

Find the value of \(\sin^{−1} (\sin \frac{3π}{5})\)

Solution :

We know that sin^−1(sin x) = x.


Therefore, sin^−1(sin (3π/5))


= 3π/5


But (3π)/5 ∉ [−π/2, π/2], which is the principal branch of sin^−1 (x)


However sin ((3π)/5) = sin(π – (3π/5))


= sin (2π/5) and (2π/5) ∈ [(−π/2), (π/2)]


Therefore sin^−1 (sin (3π/5))


= sin^−1(sin (2π/5)) = 2π/5