Question

True or false:
The equation sec2x - 2 = 0 has 4 solutions on the interval [0, 2pi).
arcsec(2)/2= 0.523598775
0.523598775+pi=3.6651914285897932384626433832795


Did i miss anything?

Answer 1

also 2pi-pi/6= 5.7595865315812876038481795360124
Is there a fourth?

Answer 2

5.7595865315812876038481795360124-pi is one but is there a fifth

Answer 3

\[\sec 2x=2\]\[\frac{ 1 }{ \cos 2x }=2\]
\[\cos 2x=\frac{ 1 }{ 2 }=\cos \frac{ \pi }{ 3 },\cos \left( 2 \pi-\frac{ \pi }{ 3 } \right),\cos \left( 2 \pi+\frac{ \pi }{ 3 } \right), \cos \left( 2 \pi+2 \pi-\frac{ \pi }{ 3 } \right)\]
\[2 x=\frac{ \pi }{ 3 },\frac{ 5 \pi }{ 3 },\frac{ 7 \pi }{ 3 },\frac{ 11 \pi }{ 3 }\]
x=?

Answer 4

Exactlly what i had, thanks :)