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General Solutions to Trig Equation

hey_its_nay

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(edited 13 years ago)

Reply 1

generalebriety

hey_its_nay

sinx=0, x=(360n)

You've missed some solutions here, haven't you? (Draw the graph of y = sin x.)

Much more crucially, though, this is wrong. If sin x = 0, you're not allowed to divide by it - but you did earlier on in your solution (implicitly, when you divided by tan x)! Notice also that if sin x = 0, cos x = +/- 1, so cos x - sin x isn't equal to 0 like you wanted. Much easier would've been to spot:
cos x - sin x = 0
cos x = sin x
tan x = 1.

As a general hint, don't divide or multiply by anything until you've made sure it can never be equal to zero. You can split it into cases if you like, e.g. "either tan x = 0 in which case .........., or tan x =/= 0 in which case we can divide by it / factorise it out to get...".

hey_its_nay

1/tanx=1, tanx=1, x=(45+180n)

This looks fine to me.

hey_its_nay

(4sin^2x -3)=0
sin^2x=3/4
sinx=+/- root3/2
x=(360n +/-60)

Again, I suspect you've missed some solutions here - in fact, you seem to have found all the right solutions for sin x = +sqrt(3)/2, but none for sin x = -sqrt(3)/2.

Try drawing the graph of y = sin x.

Reply 2

pokerplayer1191

hey_its_nay

the book says the answers are 180n+45, 360n+/-60 (got those right) and 360n+/-120
ty for the divide by zero, tht was a obvious thing i missed but do u have any idea on how to get the last solution?