Question

Find all angles between 0 and 2pi satisfying the condition cos(x) = √2 / 2

Answer 1

cos is onl positive in the first quarter of the circle\[\theta =cos^{-1}(\sqrt{2}/2)=\frac{\pi}{4}\]

Answer 2

\[\cos x=\frac{ \sqrt{2} }{ 2 }=\cos \frac{ \pi }{ 4 } ,\cos \left( 2 \pi-\frac{ \pi }{ 4 } \right)=\cos \frac{ \pi }{ 4 },\cos \frac{ 7 \pi }{ 4 }\]
\[x=\frac{ \pi }{ 4 },\frac{ 7 \pi }{ 4 }\]

Answer 3

my bad cos is positive is in the first and fourth quarters, I remember the terms in Arabic. sometimes i got confused between Sin and Cos in English. :)