Identify the graph of the equation over the given...

Transcript

00:01 So we have the parameter form as x is equal to 2 cost theta y is equal to sine 2 theta can i write cost theta as x by 2? yes, we can write it as cost theta is x by 2 and here why what is the formula of sine 2 theta? it is 2 sine theta it is 2 sine theta right so y is equal to sine theta into two cost theta i'll replace with x so y is equal to x sine theta or sine theta is equal to x by y now eliminate theta from these two equations how can you elaborate quesquered theta plus sine square is one so x square by y square plus x square by four is equal to one or i can write it as x square uh x square uh into four plus y square is equal to four y square so basically uh my curve will look like this uh it will be the equation looks like this x is equal to to plus or minus 2 y divided by root of 4 plus y square this is the function basically this is the curve we need to draw basically if you can see the powers of both x and y are even so that means this curve is symmetric the curve is symmetric about both i both x and y axis symmetric about both x sine y axis and also origin and also origin because when you replace x with the negative x and y with negative y the equation is not getting changed okay so it's enough to draw the function in the first quadrant it's enough to draw in the first quadrant so better what we do is we'll express y in terms of x because usually we write y as a function of x right so instead of x is in terms of y instead of writing x in terms of why let's write y in terms of x so we have 4 x squared uh is equal to 4 y square minus x squared y square or y square is common four minus x square is equal to four x square now y square is equal to four x square divided by four minus x square now we have four minus x squared than zero reason because y square is positive four x squared is positive so obviously this also should be positive before minus x square is positive x square minus four is negative so x should belong to negative 2 to 2.

02:35 So your graph actually belongs negative to 2 interval only.

02:39 Okay...

Question

Identify the graph of the equation over the given interval. y = -4sin \left(2x - \frac{\pi}{2}\right), -\frac{\pi}{4} \leq x \leq \frac{3\pi}{2}

Question

Identify the graph of the equation over the given interval. y = -4sin \left(2x - \frac{\pi}{2}\right), -\frac{\pi}{4} \leq x \leq \frac{3\pi}{2}

Please give Ace some feedback