4

5. Given 0 < 0 < 27 , solve sin 0 = 1.0 % 0 % 0O...

Question

5. Given 0 < 0 < 27 , solve sin 0 = 1.0 % 0 % 0O

5. Given 0 < 0 < 27 , solve sin 0 = 1. 0 % 0 % 0 O



Answers

$$ \sin ^{-1} x \leq 5 $$

In this problem. Let us look at the graph of Synnex for one period at the start of Peter. Doctor. I might do. It's a spy creeper by two Dubai and five planets. This is how the graph looks like. This value corresponds to one. This corresponds to -1. This is bye bye to and this is 552, says three power to brian cooper. This is cynics and this is X. Now let us look at what is Cynics equals to one x 5. That will be online going through this, this is Sin x equals to 1/5. And we need sign next to be less than one x 5. Which means we are looking at this region alone in the spirit. This corresponds to next belonging to by minus Simon Rows of one, my 5 two two pi plus sign in brasov, one by five. To generalize it lot to unpack. This is due in by plus by minus Sign and rules of one x 5, comma two and by plus two pi plus sign and really soft one day six that's all. And belonged to 012 and so on.

In this problem. The given equation can be read it and by dividing the equation by cause square X as five. 10 square x minus three. 10 x minus 36 Is greater than zero skin better than us. 10 x- ST into 5. 10 X plus 20 Is greater than zero Case. one is that 10? X -3 is also greater than zero and five panics Last well is written in zero from these two. We understand that The next has to be greater than three. 2nd case is that both are negative? That is The next -3 is less than zero and five clinics Plus 12 is less than zero from these two. We understand that 10 x is less than -12 by why? Now let us look at the graph of gonna fix that goes like this. This corresponds to bye bye to this corresponds to minus by writing this is turn affects and this is six Now for 10 of X greater than three. We understand that mrs Tan if X equals to treat so you're looking for this portion on for 10 of X less than minus 12 5 which is somewhere here is this Then x equals 2 -12 x five. We're looking for the region belong. So from here we get that this is just the first case X belongs to An Inverse of 3. 2. Bye bye to and from here we get that X belongs to -5 x two then in wars of -12 x five. Since 10 X has a period of by the general solution. Can you enlighten us and by minus by by two comma and by plus diamond russell -12 x five. Union key part? Yes. Them in rows of three comma here, pi plus. All right, Murky and can be 01. Doing so on. That's all.

We want to find it in this equation where teeters between zero and two parady in not inclusive of to parade in notice that this equation is a quadratic equation of scientific so we can affect the rise this equation into 73rd. Ministry sign the minus one. So we have two scientists to minus two equals zero or scientific to minus 10 So on the left side we have 73rd it's equals to three with two or scientific data is equals to one. Now. For scientific Turkish tree will do we will reject Yeah. Since santa is always founded between minus one and one for all people now. So we're left with this guy scientist that equals to one. It's easier to just draw the graph of santa between yeah zero and two pi data since teeters between zero and two pi over here we have pie here is private too. And over here is Trippi over to and for the white value is one over here and the minimums minus one. for scientists to equals to 1 72 goes, one is over here. You can see that the detail value is power to, and this is the only value between the 0 to 2 pi cycle, so therefore Dita is equals two pi over two.


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