In the study of oscillatory motion, the angular displacement of a mechanical sensor is determined to be zero when the tilt angle β\betaβ satisfies the equation
16cosβ=5.2cosecβ 16 \cos \beta = 5.2 \operatorname{cosec} \beta 16cosβ=5.2cosecβwhere 0∘<β<90∘0^\circ < \beta < 90^\circ0∘<β<90∘.
Show that this equation can be expressed in the form
sin2β=k \sin 2\beta = k sin2β=kwhere kkk is a constant to be determined.
Hence determine the smallest positive value of β\betaβ, giving your answer in degrees to one decimal place.
