<p>1)(sin^2)x-2sinx-3=0</p>
<p>2)2(sin^2)x-5sinx+2=0</p>
<p>3)2(sin^2)x-3sinx-2=0</p>
<p>4)3(sin^2)x-4sinx+1=0</p>
<p>you probably meant (sin^2)x as (sin x)^2. the notation may look like (sin^2) x but it actually means (sin x)^2. anyway, you have to factor the first part of the equation. In order to do that easily, you can consider sin x as u. it would then be:</p>
<p>1) u^2 - 2x - 3 = 0
(u-3)(u+1) = 0
u = 3 or -1 but |sin x| <= 1
therefore u = -1; sin x = -1
and by using graphs, sin x = 2n*pi - pi / 2 (general answer)
If you wanted 0<=x<=2 pi, then the answer would be 3/2 pi ONLY.</p>
<p>do the same thing for other questions, but remember: |sin x| <= 1, meaning to say
-1 <= sin x <= 1.</p>
<p>yes!
Thank you!</p>
<p>But what if </p>
<p>1)2(sin^2)x-cosx+1=0</p>
<p>2) 3(sin^2)x-cosx-1=0</p>
<p>then you use (sin x)^2 + (cos x)^2 = 1 and so</p>
<p>(cos x)^2 = 1 - (sin x)^2 and plug this into the original question.
you now solved the equation for cos x. Then, substitute cos x with u and do the same thing over. remember that for cos x it’s also -1 <= |cos x| <= 1.</p>
<p>thanks 
Where did you learn Math that well?</p>
<p>one thing I don’t get. How you transfered 2(sin^2)x-cosx+1=0 into (sin x)^2 + (cos x)^2 = 1?</p>
<p>Study Pythagorean Identities, Half Angles, Double Angles, etc.</p>
<p>whoops -1 <= cos x <= 1</p>
<p>I still have a problem: </p>
<p>2sin^2x-cosx+1=0
2sin^2x-1+sin^2+1=0
3sin^2x=0
What now?</p>
<p>i do not understand ur question. resubmit in conventional format.</p>
<p>never mind. I got it now. Can you explain me what does this all mean?</p>
<p>y=arctgx y=arcctgx</p>
<p>sinx=a
x=[(-1)^n]<em>arcsina+pi</em>n</p>
<p>If sinx=0, then x=pi<em>n (nEz)
If sinx=1, then x=pi/2+2pi</em>n (nEz)</p>
<h2>If sinx=-1, then x=-pi/2+2pi*n (nEz)</h2>
<p>Thanks!</p>
<p>that is still unfamiliar but i think they mean these:</p>
<p>y = arctangent x (shorthand y = arctan x or tan ^ -1 (x))
y = arccotangent x (shorthand y = arccot x or cot ^ -1 (x) )</p>
<p>what is n?</p>
<p>n is any integer…neZ is shorthand for the set notation that means n “is an element of” Z, where Z is the letter used to refer to the set of all integers.</p>
<p>You see this notation in the answers to many trigonometric equations. " + 2 pi n" is the radian version of “+360n” that you would use if the answer were in degrees.</p>