Sec s = 1.6948 Cos s = 0.3825 Find the value of s in the interval [0,\pi/2] that makes the statement true for each. Please explain process.

Question

Sec s = 1.6948

Cos s = 0.3825
Find the value of s in the interval [0,
`\pi`/2] that makes the statement true for each.
Please explain process.

Answer 1

that'd be true only if the value of "s" is the exact same one for both
namely if sec(s) = cos(s)
then solving for "s"
thus


`\bf sec(s)=cos(s)\qquad but\implies sec(\theta)=\cfrac{1}{cos(\theta)} \\\\\\ thus\cfrac{1}{cos(s)}=cos(s)\implies 1=cos^2(s)\implies \pm √(1)=cos(s) \\\\\\ \pm 1=cos(s)\impliedby \textit{now taking }cos^(-1)\textit{ to both sides} \\\\\\ cos^(-1)(\pm 1)=cos^(-1)[cos(s)]\implies cos^(-1)(\pm 1)=\measuredangle s`