The range of the function y=3sin⁡π216−x2 is

For y to be defined, π216−x2≥0⇒π4−xπ4+x≥0⇒x−π4x+π4≤0⇒−π4≤x≤π4∴Domain of y =−π4,π4Clearly, for x∈−π4,π4,π216−x2∈0,π4Since sin x is an increasing function on 0,π4Therefore, sin⁡0≤sin⁡π216−x2≤sin⁡π4⇒0≤3sin⁡π216−x2≤32⇒0≤y≤32∴Range of y =0,32