[tex]\bf \textit{Pythagorean Identities}
\\ \quad \\
sin^2(\theta)+cos^2(\theta)=1
\\ \quad \\
1+cot^2(\theta)=csc^2(\theta)
\\ \quad \\
\boxed{1+tan^2(\theta)=sec^2(\theta)}\\\\
-----------------------------\\\\
\pm \sqrt{1+[tan(\theta)]^2}=sec(\theta)\qquad tan(\theta)=0.1
\\\\\\
\pm \sqrt{1+[0.1]^2}=sec(\theta)[/tex]
now, which is it? the +/-? well, we know the tangent is positive, the interval we have, puts the angle on either, the 1st or 4th quadrant, now on the 4th quadrant, the tangent is negative, positive-x, negative-y
however, on the 1st quadrant, is positive, thus, the angle is in the first quadrant, and thus the secant is positive as well, since positive-x and positive-y, so is the + version
[tex]\bf \sqrt{1+[0.1]^2}=sec(\theta)\implies \sqrt{1+0.01}=sec(\theta)
\\\\\\
\sqrt{1.01}=sec(\theta)[/tex]
