# How do I understand the domain [-pi, pi) in terms of a graph? For questions such as 2sin^2x=-sinx. What quadrants are [-pi,pi)?

Relevance

In terms of sketching 2sin^2x and -sinx on a graph, -π and π are values on the x axis and thus the origin would be in the middle of the page with -π on the left and π on the right

I think you are mixing up the trigonometry angle reference quadrants (unit line rotation about the origin) with the four quadrants on your graph of 2sin^2x and -sinx.

Typically, questions like this have infinite solutions that repeat every 2π radians (ie 360°), so it is normal to restrict the solutions to one span of 2π, either by going from 0 to 2π, or in this case -π to π.

In terms of the trig quadrants this means the first and last quadrant, ie either side of the zero reference line. .

• Dixon
Lv 7
4 weeks agoReport

Correction as spotted by az_lender; it covers all four trig quadrants.

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• Dixon's answer is mostly good, but the interval [-pi,pi) includes all four quadrants, not just the first and the last.

As he said, "quadrants" are kind of irrelevant to graphing y = 2*sin^2(x) or y = -sin(x).

If you are to find x values where 2*sin^2(x) = -sin(x), you have

an obvious solution if sin(x) = 0, and in that case, the x values in [-pi,pi) are x = -pi and x = 0.  If sin(x) is NOT zero, then you have 2 sin(x) = -1, so sin(x) = -1/2 and the x-values in [-pi,pi) are x = -5pi/6 and x = -pi/6.

• Dixon
Lv 7
4 weeks agoReport

Oh yes! I'm more of a Tau guy for exactly avoiding silly mistakes like this

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• Domain -- possible values for the x variable ===  tells NOTHING about the y variable === that is called the range

[-pi, pi)  <<<  think numbers  ===  -3.14159 will be on the NEGATIVE X AXIS ... the graph might be in the 3nd or 3rd quadrants .. you do not know without knowing y values also.  ----  Pi is +3.14159 ... located on the positive x axis, again without y values you do not know what quadrant .. could be either quad 1 or quad 4

.....  remember domain only tells you about possible x values ... but a graph must have both x and y values.

simple trig graphs  like y = sin x  --- this will actually have parts of the graph in all 4 quadrants ...  you should learn this from studying trig.  the domain is -infinity to + infinity .... but the range is only from -1 to +1  ...  I know this from studying trig ... some things in math are NOT calculated, to know them you just study and memorize them.

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