287. Find the equation of the tangent to the helical line $y=a \cos t$, $y=a \sin t, z=b t$ at the point where $t=t_{0}$, and the angle it forms with the $O z$ axis.
Solution. Denoting the coordinates of the point of tangency ( $x_{0}, y_{0}, z_{0}$ ) and using the general equations (1), we obtain the following equations of the tangent:

$$
\frac{x-x_{0}}{-a \sin t_{0}}=\frac{y-y_{0}}{a \cos t_{0}}=\frac{z-z_{0}}{b}
$$

From here, the directional cosine of the angle formed by the tangent with the $O z$ axis:

$$
\cos \gamma=\frac{\dot{z}}{\sqrt{\dot{x}^{2}+\dot{y}^{2}+\dot{z}^{2}}}=\frac{b}{\sqrt{a^{2} \sin ^{2} t_{0}+a^{2}}}=\frac{b}{\cos ^{2} t_{0}+b^{2}}=\frac{b}{\sqrt{a^{2}+b^{2}}}
$$

This result shows that all tangents to the helical line form the same angle with the $O z$ axis.[^10]

In problems $288-290$, write the equations of the tangent line and the normal plane to the curve: