Consider $\mathbf I=15\hat{\mathbf x}\cos(\omega t)+5\hat{\mathbf y}\sin(\omega t)$ in Cartesian coordinates, with constant $\omega>0$. When $|\mathbf I|$ is minimum, the angle it makes with the x axis (in degrees, $0\le\theta\le180$) is ________.
Square the magnitude: $|\mathbf I|^2=225\cos^2\omega t+25\sin^2\omega t=25+200\cos^2\omega t$.
Its minimum occurs when $\cos\omega t=0$. The x component then vanishes while the y component is ±5. The vector lies perpendicular to the x axis, so the required angle is **90°**.
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