During a lab experiment, the lateral displacement LLL (in cm) of a precision pendulum is recorded relative to its resting position for small angular displacements α\alphaα (in radians). The relationship is modeled by:
L(α)=14.2+25sin(α5)+12tan(α4) L(\alpha) = 14.2 + 25\sin\left(\frac{\alpha}{5}\right) + 12\tan\left(\frac{\alpha}{4}\right) L(α)=14.2+25sin(5α)+12tan(4α)Show that for small values of α\alphaα, the graph of LLL can be approximated by a straight line, and determine the equation of this line.
