Help Solving Trig Function sec^2x+2secx-1=0 using quadratic formula over [0,360)

[shelloday]

Please help me solve the trig function sec^2(x)+2sec(x)-1=0 using quadratic formula over [0,360)

 

[stapel]

Please help me solve the trig function sec^2(x)+2sec(x)-1=0 using quadratic formula over [0,360)

Where are you stuck in plugging into the Quadratic Formula?

Please be complete. Thank you!

 

[shelloday]

Please help me solve the trig function sec^2(x)+2sec(x)-1=0 using quadratic formula over [0,360)[/QUOTE]
I plugged it into the quadratic formula and got secx=.42 and secx= -2.41.
SO do I use the reciprocal identity to get the answer? Should secx=.42 be thrown out?

Thanks

 

[Deleted member 4993]

Please help me solve the trig function sec^2(x)+2sec(x)-1=0 using quadratic formula over [0,360)
I plugged it into the quadratic formula and got secx=.42 and secx= -2.41.
SO do I use the reciprocal identity to get the answer? ..... Yes

You could have also converted to cos(x) and completed the problem with more familiar function.

Should secx=.42 be thrown out?

We know that:

-1 ≤ cos(x) ≤ 1

What does it tell you about the range of [sec(x) = ] 1/cos(x)?

 

[shelloday]

One More Question

I plugged it into the quadratic formula and got secx=.42 and secx= -2.41.
SO do I use the reciprocal identity to get the answer? ..... Yes

You could have also converted to cos(x) and completed the problem with more familiar function.

Should secx=.42 be thrown out?

We know that:

-1 ≤ cos(x) ≤ 1

What does it tell you about the range of [sec(x) = ] 1/cos(x)?

Thank you for your help, so would both of the answers I got need to be thrown out due to the domain?

 

[stapel]

...so would both of the answers I got need to be thrown out due to the domain?

What values did you get, when you converted the secant values into cosine values?

Please show your steps. Thank you!

 

[Deleted member 4993]

Please help me solve the trig function sec^2(x)+2sec(x)-1=0 using quadratic formula over [0,360)

I plugged it into the quadratic formula and got secx=.42 and secx= -2.41.
SO do I use the reciprocal identity to get the answer? Should secx=.42 be thrown out?

You got sec(x)=0.42 and sec(x)=-2.41. Now

sec(x)=0.42 gives x=arcsec(0.42)=25 degree. ..... Incorrect ... → sec(25°) = 1.103378

Again sec(x)=-2.41 gives x=arcsec(-2.41)=114.47.[/QUOTE]

|sec(x)| ≥ 1