solving sinx + 1 = secx: by graphing calculator or by hand?

[sickplaya]

Solve: sin x + 1 = sec x (0 < x < 2pi)

Is it possible to solve this question by hand, or does it have to be done by graphing calculator? I can't seem to get answer by hand, and if it can be done by hand, please show me your steps. thanks.

 

[stapel]

What have you tried so far? For instance, you converted the secant to a cosine expression, and... then what? What did you get when you checked "Y1 = sin(x) + 1 - 1/cos(x)" in your graphing calculator?

Thank you.

Eliz.

 

[sickplaya]

i can obtain the answer through the graphing calculator but i'm wondering how to do this by hand

so i have sin x + 1 = sec x
i multiply both sides by cos x
sin x cosx + cos x =1
then,
(1/2) sin 2x = 1-cos x

i dunno how to finish it off by hand i just keep going in circles

 

[stapel]

This thing is starting to bug me. The curve is nasty, but graphing Y1 = sinx+1-1/cosx clearly shows zeroes. The fact that three are at 0°, -360°, and 360° implies that at least one set of solutions should be "neat"; that is, we should be able to locate at least some of the solutions by hand.

But I'm getting nowhere. (I'm probably going through the same circular steps that you've been.) It's late, so my work would probably be suspect at this point anyway. I'll try this again in the morning....

Eliz.