Question

I need help finding all the solutions for sec x=√2

Answer 1

\(\bf {\color{blue}{ sec(\theta)=\cfrac{1}{cos(\theta)}}}\\ \quad \\ \quad \\
sec(x)=\sqrt{2}\implies \cfrac{1}{cos(x)}=\sqrt{2}\implies \cfrac{1}{\sqrt{2}}=cos(x)\\ \quad \\
{\color{blue}{ \cfrac{1}{\sqrt{2}}\cdot \cfrac{\sqrt{2}}{\sqrt{2}}\implies \cfrac{\sqrt{2}}{2} }}\qquad thus\\ \quad \\

\cfrac{1}{\sqrt{2}}=cos(x)\implies \cfrac{\sqrt{2}}{2}=cos(x)\)

so... that's a well known angle, and should be in your Unit Circle

Answer 2

thank you so much!

Answer 3

yw