Thomas' Calculus 13th Edition

$g_r=1-cosθ$ $g_θ=rsinθ$ $g_z=-1$
Take the first partial derivatives of the given function. When taking a partial derivative with respect to r, treat θ and z as constants, with respect to θ, treat r and z as constants, and with respect to z, treat r and θ as constants: $g_r=1-cosθ$ $g_θ=rsinθ$ $g_z=-1$