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(10 pts) Solve the equation for exact solutions over the interval [0, 27r) . 7) ~Ztan x = 2...

Question

(10 pts) Solve the equation for exact solutions over the interval [0, 27r) . 7) ~Ztan x = 2

(10 pts) Solve the equation for exact solutions over the interval [0, 27r) . 7) ~Ztan x = 2



Answers

Find all solutions on the interval $[0,2 \pi)$. $$ \sec ^{2} x=7 $$

So here we have an equation X squared minus seven. Express 12 equals zero and we are asked to solve this equation graphically. So I have used as most and free online graphing calculator to graph the two functions. So what I graft is why equals X squared? Why equals X squared my seven X plus 12 and why equals? And we're supposed to see where the two lines intersect, because that is where they will be equal to each other. And if we look here, we can see the Intersect two points here and here. And those points are X equals three and X equals for so that means thes will be the solutions to the equation.

I'm going to solve this inequality like I would solve an equation. So I'm going to try to isolate X. First thing I would do is add seven to both sides, so that gives me two. X is less than or equal to 28 and then I'll divide both sides by two. So X is less than or equal to 14. Now I want to give my answer in interval notation. So I want to have a closed bracket around me 14 to show I'm including it. And because we're going less than 14 we're going too negative Infinity. So we have the interval that starts at negative infinity and goes to 14.

Hello, everyone. Today we're going to solve a problem. Number 48 here. We need to find a solution off. Three six correx plus four Costco Rx equals seven. So three developed by cause cortex plus four cause Corrects because seven three plus four cause rest of forex it goes seven cost clerics for causes to forex minus seven cause correx first three because zero So we can split in tow like four called square X minus three cause Kerekes minus one Because zero we get calls six equals plus or minus toe three by two or Cossacks Because that's a minus. Smart X equals by basics five by by six and seven by basics and 11 bye bye six or X equals zero comma pie Tradition off the equation between zero comma Bye Will be zero five by six. Fight by by six Bye seven by by six and 11 by by six. Thank you

Okay, so the first thing that I noticed is cosine represents X and cosign is positive. So when is the X axis positive? And what quadrants? Well, it'll be on the right side. So in the first and the fourth quadrant and then the second thing I noticed is that when cosine equals square to three over to my reference angle will be 30 degrees in degrees. So my reference angle distance from the X axis, too. Theatrical angle will be 30 degrees. So in quadrant one, my angle will just be 30 degrees. And then in Quadrant four, I started 360 degrees and I'm going clockwise 30 degrees. I'm subtracting 30 degrees, so my second angle will be 330 degrees.


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