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Z02OSP-MATH-1316-83001 Homework: Section 8.6 Hon Score: 0 of 1 pt 8.6.91Find the exact value of sec 2 tan169 120sec 2 tan 12 (Simplify your answer; including any ra...

Question

Z02OSP-MATH-1316-83001 Homework: Section 8.6 Hon Score: 0 of 1 pt 8.6.91Find the exact value of sec 2 tan169 120sec 2 tan 12 (Simplify your answer; including any radicals . Use integers or fraction:

Z02OSP-MATH-1316-83001 Homework: Section 8.6 Hon Score: 0 of 1 pt 8.6.91 Find the exact value of sec 2 tan 169 120 sec 2 tan 12 (Simplify your answer; including any radicals . Use integers or fraction:



Answers

In Exercises $107-110,$ find the exact value of each expression. Do not use a sqlculator.
$$
\sin \left(2 \sin ^{-1} \frac{\sqrt{3}}{2}\right)
$$

We are us to solve the tinges of 105 degrees using or half Ingle identity for tension, which, as you can see, every here says that the tangent of X over two equals one minus coastline X over Cenex. So first we're trying to figure out what X is. So in this case, it's just going to be 105 times to let's just write that as dot so it's less confusing. And 105 times two is 210. So 210 is our axe. So now we can insert this into our equation. This is going to be tension of 200 ton over to which is just our way of re writing. 105 equals one minus coastline of to turn over side of two ton. Now we can insert our values of Costa into town and signed two ton into this identity. And once we do that, we end up getting one minus in Costa into 10 is negative for out 3/2 so we can insert that in in sign of to 10 is negative 1/2. So now that we have this, let's do a little bit of simplification so we can turn our one into 2/2, and then the negative times a negative becomes plus sign. So this becomes to over two plus rather 3/2 over negative 1/2 which becomes two plus red three over to and then all of that is divided by negative 1/2. Or, in other words, we can write that as times negative too. So now both of these twos cancel out over here. So now this becomes negative too. Minus rab three. Since that negative sign is multiplied to both of these since that was negative one that was left over here. So this is our answer.

We're us to solve the tension of 75 degrees, using 1/2 England 10 to eat. So one of the half Ingle identities for tinges says that tinge it of X over two equals one minus co sign acts over sine X. There's another one, but we're just gonna be using this one for now. So first of all, we have to figure out what 75 times two is. That's going to be our first up, since that is what we're going to insert into our half Ingle identities. So 75 times two is 1 50 So that's what we're going to right over here. So this is going to be Tanja of 1 50 over to, since that's just our way of rewriting 75. And then we're going to insert 1 50 into this equation or this identity. So that's going to become one minus costar in 1 50 over sign of 1 50 So we know looking at our unit circle, that co sign of 1 50 is just going to be negative rod to or negative 3/2 so we could add that in and then sign of 1 50 if we will get our unit Circle is five pi over for sorry is 1/2. So now let's simplify this. This is going to become one plus red 3/2. Or if we make this, we can rewrite this as to over two, plus Route 3/2. And that's just going to become two plus Rob 3/2. And then we're dividing that by 1/2. Or, in other words, multiplying this by two. So this is the tubes they're gonna kids'll over here. So this becomes two plus Rob three. So this is our answer and is the tinge of 75 degrees using or half Ingle identity for a tendril?

We know that this I am the rebar out of chewy, could you minus one so minus tension The money ain't by divine victory Plus the course I off the modest five by act of sex. So the next time you need to do is we need to find the reference reference angle on this one and this one this well, so we do in on this I now and the widow minus eight by 10 three. I ain't even gay. Three will be modern June so means now we need you and one complicity co here to add to run here. So we could you AA minus six. We menace to buy out of a tree. So where we judge blocked ID here? It would be a ghost club to buy three. So should be in the third contract here. There's only beam honest to buy out of three. And the reference angle would be this one here, presumably the Tita Prem don't eat a prime. We go to buy one stoop I have a tree so equal to buy the victory. So we had the first preference anger And now and for the second angers him. Have Manus five by six. And here we can try directly here minus five by six. So it goes clockwise, So I should be in the third quadrant. Yeah, this will be minus five by number six. And the reference ang go shouldn't be in this one hand is in with the Bram and to the primacy ico Jew by minus five by undersexed So every go Jew by over six toe found all of them now in Disney go to minus tension now found 1/3 quarter in that the tensions dies Does value positive So which turned this month's I'd planned to be there by that tree Plus ghosts I off for the month five by six The kose items to be negative So hard to win a minus in front now And the anger becomes the bite of sex And now we know the dungeon invited dream We go to the site off by trade even because I'm the bite of three my nose Because I'm the kind of sex we go Thio sweet victory over too And now we go to minors Side driver three We go Thio screwed up a tree And with Ju dividing by the cause I am behind the tree. Could your half and my escort the tree ever too. So you should get equal to minus spreading tree in Tokyo division will be the multiply by the reciprocal to over one and a manuscript of a three over two. So we get Geico Jew minus two Castle Owner George, I have to go. The three minus grade. The tree. Amber too. So you're willing. Assembly nominated Joe here. And every Gonda managed to scrape the three minus square the tree. So I was gonna echo Jew Ministries, could three. I'm with you, and that's dancer.

Okay, so we'll find the numerical value of our expression here by using the definition of hyperbolic canyon. So that's equal to, um, hyperbolic sign over hyperbolic co sign. Okay. And we know that type of all X sign that's equal to easy carbs, Errol. Minus Use it of our negatives, Earl. Over two all over. Hyperbolic co sign, which is eating up power zero. Plus. He took part of negative go over to. So what does that give us yet? Um, one minus one. So that 0/2 over to over to. So that gives us zero. Okay. And now it's fine. Have brought a ton of one again. That's people to I hope you're bolic fine over hyperbolic coastline. So that gives us each a part of one minus eating part of negative one over to all over each of her. One morning or start, it's plus easy carve. Negative one over to. Okay, so we're left with, um, he minus easy to carve. Negative one over e one plus easier part of negatively


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