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T If tan 0 = and 0 < 0 < find cos 0. 2 2COS 0 =...

Question

T If tan 0 = and 0 < 0 < find cos 0. 2 2COS 0 =

T If tan 0 = and 0 < 0 < find cos 0. 2 2 COS 0 =



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If $\tan t=\frac{12}{5},$ and $0 \leq t<\frac{\pi}{2},$ find $\sin t, \cos t, \sec t$ $\csc t,$ and $\cot t$.

Okay, So being between pyre or two and pie is telling me that were in the second quadrant. So we're somewhere over here. I don't know exactly where. I'm just giving you a visual. Um, and then sign. I think they used t. Uh, if you think about it on the unit, not the unit circle. But just think of sign is being opposite over the high pot use. So Route three is ah, the opposite. The hypothesis for So then if you want to figure out what this call this X because it's on the X squared X squared, plus Route three squared equals four squared. I think intel. I'm using the the thuggery and serum here. Um, so x squared plus three is equal to 16. So x squared equal 13 as you subtract over. So this distance is negative. Route 13. So then, as they ask you to figure out what tainment is, um, well, tangent in the second quadrant is negative. So tangent of tea would equal the opposite over Jason. So three over route 13. And if your teacher is accepting of that answer, then you can leave it. If your teacher expects you. This um, rationalize the denominator. Just multiply. Topping Bounded by route 13. So negative three times 13 is Route 39 over 13 is ah rationalized answer.

This is a problem 101 in problems at 4.2 of the Blitzer pre calculus on this one, we have to determine which of the following is true if pie is less than tea, which is less than three Piper to that means the angle is between pie and three Piper, too. Which of the following me is true? To help us determine which of the following is true, let's go ahead and draw our unit circle. Figure out where those angles are. So here's zero pi over too pie and three poverty. So here's pie and three pi over too. So we're interested in quadrant three. So let's put a point out here on our unit circle and draw our triangle. Drop it perpendicular to the ex access to finish out our right triangle. Remember, this point ends at some ordered pair x y, uh, ex being along the x axis And why being in the direction of the Y in this case because of where we are, the ex goes to the left, which makes it negative. The why goes down, which makes it also negative. The hype on news is one, so we should be able to determine the values of the sign. The co signed the tangents and all the trigger functions. Using that information, at least we can determine their signs that I mean so the sign of that angle t if it ends up in between pie and three pi. Over too, is the opposite side over the hypotheses, the opposite side being the why the hippopotamuses one. The why is negative. So the sign of that angle is negative, so that's less than zero. The co sign of tea would be the adjacent side over the high pop news. The adjacent sides is X Y. Pop news is one. The X is also negative, so that's negative. The tangents is the opposite side of the adjacent side. The opposite side is the why Jason Side is the ex. They're both negative. So that's a negative over another negative, which is positive. So the tangent is positive. The sign and the co signer, both negative. Okay, let's see if we can figure out what makes sense in our statements here. So statement, eh? The sign of tea is greater than zero. Um, that would not be true, because the sign of tea. We figured out down here is negative, so that would be less in zero. Not true. Statement Be The sign of tea is less than zero. That's true because it is negative. The tangent of tea is less than zero. That's not true because the tangent of tea is positive. Statement. See, the tangent of tea is greater than zero. That's true because it's politics. The co tangent of tea is greater than zero. Well, the co tangent is the reciprocal of the tangent. If we have a positive value for the tangents, the reciprocal should also be positive. If the tension is y ver x, the co change it is X over why that's still a negative of a negative, which is positive. That's true. Let's check statement D. Anyway, Even though I think we have the answer, the tangent of tea is less than zero. No, that's not true, because we determined that danger of tea is positive, so that would be greater than zero. So statement C is correct and take a look. It's how we drew out our work with Unit Circle to determine how we know that That's correct

Yeah. In this problem we have given the equation Tangent to T -2 into society is equal to zero and we are asked to find the solutions of the equation that are in the interval zero comma to buy. So we have Attention to T -2. Into Society is equal to zero. By using the pragmatic function we can write engine to T as signed today upon. Co sign to t -2 into society is equals to zero. Now by using the techno metric formula of science duty we have scientology is equal to you. Went to see I intend to co sign thing Vi get to into society into a society upon because I into b minus two interco scientists. It was 20 by taking two interco scientific common. We get to enter society into sci fi upon Because I into T -1 is equal to zero by taking each factories equals to zero. We get because scientists equals to zero. All 70 Upon goes into T -1 is equals to zero. Further we get Society is equal to zero or 17 minus Consigned to be is equals to zero by simplifying it. We get do into science where the plus 70 -1 is equal to zero. It would be equals two To win 2 17 -1 In two. Scientific Plus one is equal to zero. No hell we have. So scientists equals to zero. All Science is equal to one upon to all. scientists equals 2 -1 because scientists equals to zero. It implies that They would be equals two by upon to Coma three by upon to or scientists equals to one a point to. It implies that They would be equals two by upon six comma by minus by upon six go on. Scientists equals 2 -1, implies that They would be equals 2 3 5.2. Therefore we get These equals two pi upon six comma by a point to coma 5 5.6 comma three by a Pontoon. These are the solutions

Yeah. In this problem we have given the equation Tangent to T -2 into society is equal to zero and we are asked to find the solutions of the equation that are in the interval zero comma to buy. So we have Attention to T -2. Into Society is equal to zero. By using the pragmatic function we can write engine to T as signed today upon. Co sign to t -2 into society is equals to zero. Now by using the techno metric formula of science duty we have scientology is equal to you. Went to see I intend to co sign thing Vi get to into society into a society upon because I into b minus two interco scientists. It was 20 by taking two interco scientific common. We get to enter society into sci fi upon Because I into T -1 is equal to zero by taking each factories equals to zero. We get because scientists equals to zero. All 70 Upon goes into T -1 is equals to zero. Further we get Society is equal to zero or 17 minus Consigned to be is equals to zero by simplifying it. We get do into science where the plus 70 -1 is equal to zero. It would be equals two To win 2 17 -1 In two. Scientific Plus one is equal to zero. No hell we have. So scientists equals to zero. All Science is equal to one upon to all. scientists equals 2 -1 because scientists equals to zero. It implies that They would be equals two by upon to Coma three by upon to or scientists equals to one a point to. It implies that They would be equals two by upon six comma by minus by upon six go on. Scientists equals 2 -1, implies that They would be equals 2 3, Therefore we get These equals two pi upon six comma by a point to coma 5 5.6 comma three by a Pontoon. These are the solutions


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