GATE Electronics and Communications (EC) 2016 Shift 2 Solved Paper

Consider the time-varying vector $\mathit{I}=\hat{\mathit{x}}15\cos \left(\mathit{w}\mathit{t}\right)+\hat{\mathit{y}}5$ sin(𝜔𝑡) in Cartesian coordinates, where 𝜔 > 0 is a constant. When the vector magnitude |𝐈| is at its minimum value, the angle 𝜃 that 𝐈 makes with the 𝑥 axis (in degrees, such that 0 ≤ 𝜃 ≤ 180) is ________