The problem is:
Vector E is given by
$$E = \hat{R}5Rcos(\theta) - \hat{\theta}\frac{12}{R}sin(\theta)cos(\phi) +\hat{\phi}3sin(\phi)$$
Determine the component of E tangential to the spherical surface $R = 2$ at point P($2$,$30^\circ$,$60^\circ$).
The solution to the above problem is (according to the solution manual):
At P, E is given by $$E = \hat{R}5(2)cos(30^\circ) - \hat{\theta}\frac{12}{2}sin(30^\circ)cos(60^\circ) +\hat{\phi}3sin(60^\circ) = \hat{R}8.67 - \hat{\theta}1.5 + \hat{\phi}2.6 $$
The $\hat{R}$ component is normal to the spherical surface while the other two are tangential. Hence $$ E_t = -\hat{\theta}1.5 + \hat{\phi}2.6 $$ End of solution
Now my question is, how do you know which components are tangential and which are perpendicular.
Because this is in relation to a sphere, where $\hat R$ is the direction of the radius from the center of the sphere, $\hat R$ will always be perpendicular to the sphere. hope this helps