Question

Use a graph to solve the equation on the interval
[−2π, 2π].
(List the solutions in increasing order from left to right on the x-axis.)
sec x = sqrt 2

Answer 1

Not with a graph but to help explain.
\[\text{The secant of an angle is the multiplicative inverse of its cosine.}\\
\ \ \ \sec x = \frac1{\cos x}\\
\ \ \ \sec x = \sqrt 2\\
\ \ \ \cos x = \frac{\sqrt 2}2\\
\text{We know the unit circle identity states...}\\
\ \ \ \sin^2 x+\cos^2 x=1\\
\ \ \ \sin^2 x+(\frac{\sqrt 2}2)^2=1\\
\ \ \ \sin^2 x+\frac12=1\\
\ \ \ \sin^2 x=\frac12\\
\ \ \ |\sin x|=\frac{\sqrt 2}2\\
\text{Now we know the angles have a positive cosine which is equal}\\
\text{to the absolute value of the sine. What angles satisfy this equality? (think)}
\ \ \ \frac\pi4,\frac{7\pi}4
\]

Answer 2

http://prec.alcul.us/wp-content/uploads/radian-unit-circle.gif

Answer 3

Sorry I'm still confused. I understand a little bit with the unit circle, however, how do I make the equation: \[\left| \sin x \right| = \frac{ \sqrt{2} }{ 2 } \] into (x,y). Thanks!