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Tting StartedUnproctored Placement AssessmentLet 0 be an angle in quadrant III such that cos0 = 13 Find the exact values of cSc0 and cot0.csc 0Xcot 0...

Question

Tting StartedUnproctored Placement AssessmentLet 0 be an angle in quadrant III such that cos0 = 13 Find the exact values of cSc0 and cot0.csc 0Xcot 0

tting Started Unproctored Placement Assessment Let 0 be an angle in quadrant III such that cos0 = 13 Find the exact values of cSc0 and cot0. csc 0 X cot 0



Answers

Find all trigonometric function values for each angle $\boldsymbol{\theta}$. $$\csc \theta=-3, \text { given that } \cos \theta>0$$

Base. If this problem were given that co seeking of data is equal to three, we're also told, but CU tangent of fada is less than zero. So first we have to figure out which quadrant these trig functions would be found from. So we have. We can use this acronym. All students take calculus. Where in the first quadrant, all trick function values air positive in the second quadrant, only sign and co seeking values or positive. In the third quadrant, only Tangent and Coach Hanjin values air positive and the fourth quadrant on Li co sign and seeking values are positive. First, we have that CO seek in data is equal to three, which is obviously a positive number. So our only two options right now are quadrant two in quadrant one. Because that is, those are the only two quadrants where co seeking is positive are second or second condition. Is that co tension of data is less than zero, meaning it's negative. The only place where co tangent out of these two quadrants is negative is quadrant two. So with this, we can actually make a new coordinate plain with one right triangle where this is data and we have that coast seeking of data is equal to three co seek in is the inverse of is actually the reciprocal of sign So sign is opposite overhype autumn useco seek It would be high pod news over the opposite. So the high pontin use is three and the opposite is one not to figure out the other side we can simply use We can simply use the Pythagorean theorem. So we have three square minus one squared is equal to b squared now where three squared would give us sorry nine You just undo that it would be nine minus one is equal to B squared. So be would obviously be the square root of eight here though the side would be the negative squared of eight because this x value goes to the left. And now with this, we can actually figure out the rest of the trig functions. So let me just erase this so I get a little more room. So first we already know that co seeking If data is equal to three, this means that sign of data which is the reciprocal, would be equal to 1/3 the coast sign of Fada is the adjacent over the high pod news, which would be negative squared of eight over three. The secret of data, which is simply the reciprocal of co sign, would be three over the negative square root of eight. The tangent of data is opposite over a Jason should be one over the negative square root of eight and the co tangent of Fada. It's simply the reciprocal of that. So it would simply be the negative square root of eight and these six trick functions for our final answer to this problem.

Here we are given me Casa, Get off! Twitter is equals to three and court off Florida Less than zero We know that caustic went off data is positive in the second quarter and in first quarter. But in first quadrant Companion off trita is also positive. Therefore, hair tits allies in the second quarter. So we will, right? Data is in second Cordant No, we know that Corsicans after ties one by science data. Or we can say that scientists is one by cause he can't off titter. So from here we will have scientific physical stoke one upon three. No, we have the properties like court engine scares X is it questo cause against scared X minus of one. So here we will have court scare Tita, is it calls to goes against care? Tetteh minus one. This will be cool toe three scare means nine minus off one. So we will have court. Argentina is called oh minus off to root toe as Cordiant, its allies in the second cordant and it is negative in the second quarter. No en gente is given by run a bone court engine off data so this will be equal to one upon minus off to root toe. This can be also written as minus off Roto A bone four. So we have tantalizing calls to minus off Ruto by four No, we will determine the value off course Titter So course data is equals to sign theta a born off 10 gente de so this will be equals two one a bone three a born off minus Ruto by four This will be equal dough four by minus off three group to we can write it as minus off to Ruto by three No, the value off sick and tater is given by one a bone off course Sida. So this will be cool. Store one by minus off photo by three So this will be close to minus off. Three roto over four No lex vehicle. All the values we have determined we have scientific physical 21 by three courted eyes equal to minus off Toto Daniel Day after day is equal to minus off Route two By four course off theta is equal to minus Toto by three and second after ties equals two minus off three roto by four

In the question, we have to find the Riemann Integral Metric functions. The given to dramatic function is court off three tricycles minus two where theater terminates in the quadrant. Second, now moving towards the solution for the Given Technomic took place. Cocoa Arteta Rx will be called minus two and why will we call toe one? So our will be given by plus minus off in the road minus two squared plus one square, which will be plus minus, wrote five now as the three title minutes and question toe. So all the ratios except Sign Pita and Uh, course said data will be negative on these two will be positive. So now finding the other ratios signed data will be given by white divided by R, which will be won by through five. Cost data will be excavated via which will be minus two by route fight. Then Keita will be minus one by two. Uh, sad data will be are divided by eggs which will be minus root by five minus the road five by two cause sack off data will be road five and this will with this solution to the given question. Thank you

So in the given question, we are told to find the exact value of Kosik of 13 by by train. Right? So we are going to find the value using the unit circle graph, which is given. Right? So how do we find the value? So the first step is to locate the point that is 13 5 by three units from zero. Right? So 13 paid by three units in the past year direction from zero. So how do we move 13 5 by three units in the past year direction? So we can simplify 13 5 by three and write it as 12 5 by three plus by by three. Right? And now it is easy to find because 12 5 by three is actually 45 Right? So 21 divided by three is four, so 45 plus by by three. So in the next step, what we're going to do is to start from zero, move in the past two direction forward by units first. So this this is by next don't bite then three pi And then 45 So now that we have reached fought by over here Next we have to go by by three units more. Right? So let's go by by three units more from zero. So we will reach the point by by three on the graph. Right? So this is actually showing us that the 13 5 by three units as same as moving. It is same as by by three units in the positive direction. Right? So it receive us moving by by three units in the positive direction. And the coordinates at this point are one by two and group three by two. And what this coordinates gives us is the cause and sign value of the required angry. So the cause of 13 by by three is the X coordinate. And the sign of 13 by by three as the Y coordinate, right? So now that we have the cost and sign values, we can use an identity that says Kaseke of an angle tita can be found as one by sign of that anger. So using this identity we can set that proceeds of 13 by by three is equal to um is equal to bye bye sign of 13 by by three. Right? And we have the value of 13 sign of 13 by by three as root three by two. So one by route three by two is actually to buy road trip. So this is the required answer. So I hope you understood the method. Thank you.


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