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Find € for 0" s0 360cos B= 0.29, tan 8 < 00 = (Use a comma to separate answers as needed Round to two decimal places as needed. Do not include the deg...

Question

Find € for 0" s0 360cos B= 0.29, tan 8 < 00 = (Use a comma to separate answers as needed Round to two decimal places as needed. Do not include the degree symbol your answer:)

Find € for 0" s0 360 cos B= 0.29, tan 8 < 0 0 = (Use a comma to separate answers as needed Round to two decimal places as needed. Do not include the degree symbol your answer:)



Answers

Solve the given trigonometric equation on $0^{\circ} \leq \theta<360^{\circ}$ and express the answer in degrees to two decimal places. $$\cos ^{2} \theta-6 \cos \theta+1=0$$

In this video we will find the value of theater. Using the equation cosine squared theta minus six coastline data plus one equals zero. To solve this equation, we can substitute in X. For cosign theta which gets us X squared minus six. X plus one equals zero. And then we can use the quadratic formula to find X Which is 5.83 or 0.17. So Cassandra is equal to 5.3 or .17. However, coastline data cannot be greater than one. So this just leaves us with cosign data equals .17 and we can use our calculators to find that. That means that data is equal to 80.12°. Looking at this unit circle here. However, you can see that if this is the angle and the spot on the X axis shows the coastline value. We can see that this angle also has the same co sign data value and we can find that angle. All right, subtracting This angle here, the 80° from 3 60. And we find that that angle is to 79.88°. And so these are our two final answers

Alright. The reason I'm going straight to a graphing calculator is um it's not a fact, terrible problem. Um I also need to make sure I change my mode 2° and probably to zoom out quite a bit Because we want answers actually can just change the settings between 0 360°.. Mhm. Anyway uh so we have tangent squared, I'm going to call it X. Instead of data. What else do we have? I'm sorry. It's two tangent squared minus tangent of data. Yeah. And then uh -7. So what I'm looking for is aware that curve is equal to zero which is clearly the Y. M sorry the X. Axis. So you're looking at 64.928 degrees. Um 19:21.413 244.9- eight. Yes. And then 301.413 and all those are in degrees. Um So what you would have to do if your teacher is adamant you have to show work is you'd have to use a quadratic formula, it'll be tangent of X. Which is equal to negative B plus or minus. And I'm gonna write all that out, but it's a square root of B squared one minus four times a times C. All over to a two times 2. And you tell I'm getting half my answers here. Um because I'm missing the minus in there, so plus or minus the minus gives me the other answers. Uh And then the last thing is I just copy this what actually actually X. X would equal in verse of that whatever those values are. And then you have to either add 180° or subtract 180° until you get to these four correct answers. Get that other one in there for you. So six? That's I mean that's pretty straightforward and you just have to do it multiple times and you already have the answers

In this video we will find the value of data using the equation two times tan squared of theta minus tangent data minus seven equals zero. We can start by substituting an X. For tangent data and then finding the value of X. Using the quadratic formula and getting that X Is equal to 2.14 or 1.64. This means that tangent data is equal to 2.14 or negative 1.64. Which we can use our calculators. And find that that means that data is 64.93° or negative 58.59°. To find the equivalent to the angle -58 Degrees. That's between zero and 360. We can subtract 58 from 360 and find that the angle is 301.41°. two. Additional angles that have the same tangent values as these angles are the angles in their opposite quadrants. So they have the same science data and co sign data values, but the negatives of the original science data and co sign data values. So about here and about here. And to find these angles, we can first do 1 80 plus 64 get to 44.93 and 1 80 minus 58 get 1 21.41. And so these are our solutions

Okay, I went ahead and type this equation in already. Um, the part of the reason why I'm using a graphing calculator here is that this is not a fact herbal problem. There's no factors. One that adds to be negative six. So you could use a quadratic formula. Um, but you'd eventually need a graphing calculator, so you might as well just kind of use it the way I'm using it. Now, the problem with what I've done so far is ah, where this these equal zero. This is written in radiance. So you can take these answers and convert him two degrees, which is, you know, 1.398 and you just multiply it by 1 80 over high and you'll get the correct answer. You're looking for 80.10 degrees. The other option, though I just learned this today you can actually change us to be in degrees. Only thing is, you would want to change your bounds to be, um I'll just go to 400. Not what I wanted on the X axis to go to 400. It's too much. And so when you look at this, you know, earlier I said my answer would be about 80.1. Uh, because I rounded here. We get slightly different. Answer. 80.12 is a better answer, and 279.88 degrees are your best two answers. So if you're second guessing me because my answer here is a little off, it's because we rounded 1.398 So it's off just a little bit better Answers. 80.1 to 1 and 279.879


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