Determine θ in decimal degrees, 0° ≤ θ ≤ 90°. Round results to an appropriate number of significant digits.
sec θ = 1.5
answer = 48 degrees
how do i get to this answer?
recall: $\displaystyle \sec \theta = \frac 1{\cos \theta}$
so, $\displaystyle \sec \theta = 1.5$
$\displaystyle \Rightarrow \frac 1{\cos \theta} = 1.5$
$\displaystyle \Rightarrow \cos \theta = \frac 1{1.5}$
$\displaystyle \Rightarrow \theta = \cos^{-1} \left( \frac 1{1.5} \right)$
now plug that into your calculator (remember to put it in degrees mode this time )