# Dimensional Analysis Quiz 5

See if you can determine the dimensions of "$k$" in each of the following (where $x$ is a distance, $R$ is a radius, $h$ is Planck's constant with SI units of joules x second, $f$ is frequency and $T$ is absolute temperature):

1. $sin (kx)$
2. $10^{kx}$
3. $cot (kx^2/R)$
4. $e^{hf/kT}-1$

1. dimensions of $k = L^{-1}$
2. dimensions of $k = L^{-1}$
3. dimensions of $k = L^{-1}$
4. dimensions of $k = M\cdot L^2\cdot T^{-2}\cdot \theta^{-1}$
NOTE:  In 4, $k$ is the Boltzmann constant, which has a value of $1.3 \times 10^{-23} J/K$.