SOLUTION: Will you please solve the following equation and find all solutions? And provide an explanation? I am not sure whether to write it this way: {{{ 2sin(x)^2 + 3sin(x) + 1 = 0 }

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Question 437811: Will you please solve the following equation and find all solutions? And provide an explanation?
I am not sure whether to write it this way:

or this way:
2sin^2(x) + 3sin(x) +1 = 0
Thank you
Found 2 solutions by ewatrrr, solver91311:
Answer by ewatrrr(24785) (Show Source):
You can put this solution on YOUR website!

Hi
2sin^2(x) + 3sin(x) +1 = 0
factoring
(2sinx +1)(sinx + 1) =0
(2sinx +1)= 0
sinx = -1/2
(sinx + 1) =0
sinx = -1
See following (cosx,sinx) summary for the corresponding solutions for the above

Answer by solver91311(24713) (Show Source):
You can put this solution on YOUR website!

2sin^2(x) + 3sin(x) +1 = 0 is correct, or you could have done

But either way, I got the picture.

Let

Then by substitution

Factor

Hence:

or

Substituting back:

or

Use the unit circle, remembering that the -coordinate represents the value of

So if

then

but you can go around the circle as many times as you like, so all of the solutions for that same terminal point on the unit circle are given by:

where

likewise

and in the case of

John

My calculator said it, I believe it, that settles it