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Use identities to find the exact value of the indicated trigonometric function of the acute angle 0.Ruthagerean Identities t? 0+0220-1I+42 ~e2 01+08-04114} sin 0 =c...

Question

Use identities to find the exact value of the indicated trigonometric function of the acute angle 0.Ruthagerean Identities t? 0+0220-1I+42 ~e2 01+08-04114} sin 0 =cos 0 = 4Find tan 0.

Use identities to find the exact value of the indicated trigonometric function of the acute angle 0. Ruthagerean Identities t? 0+0220-1 I+42 ~e2 0 1+08-041 14} sin 0 = cos 0 = 4 Find tan 0.



Answers

Use the given value and the trigonometric identities to find the remaining trigonometric functions of the angle. $$\tan \theta=-4, \cos \theta < 0$$

Okay, so this problem were given that coast on its data is equal to negative 1/4. And we're also told that tangent of data is greater than zero and were asked to figure out the exact values of the other. Trick functions. So first, let's figure out which coordinate which quadrant trick functions would be in. So we can remember all students take calculus. Where the first quadrant, all the trick functions air positive. In the second quadrant, Onley, sign and co seeking are positive. In Third Quadrant, Onley, tangent and co tension are positive. And in the fourth Quadrant, only co sign and seeking are positive. So we're told that code co sign of data is negative 1/4. So obviously that's a negative answer. So it won't be quadrant one because every trick function is positive there, and it won't be quite and four because co sign is positive there. And now we're also told that tangent of data is greater than zero, which means that it can't be quadrant two, because tension if data would be negative there. So our answer is quadrant three, and now we can make a new coordinate plain where we can grab a right triangle to help us figure out the other trick functions. So we know it's in quadrant three and the right triangle would look something like this where this is data and we know that the co sign if data is negative 1/4. So that's a Jason over a high pot News. This is the adjacent and the hype on uses right here. We can figure out the other side using the factory and the're, um we have four squared minus negative. One squared is equal to B squared where b is that one side. So we have 16 minus one is equal to B squared, so be would be the square root of 15. But this year would be the negative square root of 15 because it is a negative y value. So with this, we can figure out the all the other trick functions. Sorry. Let me just rolling. Okay. So, me you raised this so I can write the trig functions there first. We already know that the coastline of data is equal to negative 1/4 and then the seeking of data, which is simply the reciprocal of this would be equal to four over negative one, so that's just negative. Four. We have the sign of data, which is the opposite over the high potting use, which would be negative squared of 15 over four and then the coast. Seeking of Fada is the reciprocal of this. So that's four over. The negative squared of 15 tangent of data is upset over high pot in use. Sorry opposite over adjacent. So that's negative squared of 15 over negative one. So that's just square to 15. And then the co tangent of data is the reciprocal of that. So that's just one over the square to 15 and these six trick functions for our final answer.

Here we are given with course, off data is a close to minus off one by four and we have a penchant off data greater than zero. We know that pendant off their ties positive in only first and third quarter, but cost it ties. Old supportive gave in first quarter. Therefore Theta lies in third Gordon. No, You know the property signs. Scared topless. Go scare today is equal to one. Therefore from the property we will have sand Scattered eyes equals to one minus off course. Scared titter. So this will be cool. Toe one minus off. Minus one by four Hold scare. This will be cool. Toe 16 minus of one by 16 is equal toe 15 way 16 We will have sign off. Theta equals two minus off road 15 upon for as scientist eyes negative in the third cordon. No, we have developed off scientific data. And Costa therefore Syngenta will be equals two sign off the door. Forward goes off Florida. So this will be cool toe minus off road 15 over for a bone minus off. One by for this will be called Oh, rolled off 15. No, we will have contingent off Twitter. It calls to one a bone pensioned off to Dr So this will be close to fun upon wrote off 15 or we can say rode off 15/15 we will have second. Tita is equal store van. A phone goes off titter so this will be close to one A bone minus off one by four and this will vehicles took minus off for also course. Second off Twitter is given by one a bone scientific data. So this will be called oh one A bone minus off road 15 over four. This will be close to minus off four upon road 15 or we can say minus off. Four road 15/15. So we have find out devalues off all the five thermometer functions which are given by sign off their ties equal to minus off road 15 by four tangent After ties Equal door old 15 contingent off today Isaac Waldo Road or 15 by 15 second After ties equal to minus four and consequent off their ties equal to minus off. Four through 15 by 15

This problem by to fire in which we need to use the fundamental identity to find the remaining diplomatic functions give in 20 tickle toe minus three before and science data greater than zero. So let us first ascertain the quadrant in with it. Allies. 22 miles. Three before so 10 theater negative. So current must be to. And food scientific. Positive quadrant must be 1st and 2nd common quarante days second. So Tita belongs to quadrant toe. Okay, now we have 10 theater minus three before so we have Patagonian identity six square Tita minus transcribed theater equal to one. So 60 it'll be plus minus one Palestinian squad, Tita. Okay, so we'll be using this. Identity Secretary will be cool toe plus minus now. Uh, since utilizing current too so sick data must be negative. One place minus three before whole square. That is minus one plus nine by 16. That is minus five per four. So sick, Tita, His minus five before cause Dita will be reciprocal of spectator. That is minus 455 Okay, we have 10 deter. We have got cost theater. We have six theater so we can find card data. It will be equal toe one by 10 Theater That is minus four by three No, according to quotient. Identity we have? Yeah. 10th the tickle toe. Scientific data. My cost data. So from here, scientists will be equal to 10th return to cause theater. So, scientists, I will be equal to 10. Theater means minus three before into cause theater. We already have, I think. Yes, Minds for about five. Okay, so four and four will get cancel out. So scientific will tow three by five and Kosik treatable Reciprocal of scientific data one by scientific data. So five by three. So these are the remaining traumatic functions. Thank you.

It is given to us there. Thank you. Music was for Valtteri and caused puta is less that deal. So this implies Do you tell lies in our country Because in Cordant three costume would be negative on tend to be positive and we're supposed to find the remaining five trigonometry functions. So if you represent this given permission on the Cardinals excess plane we have instances on by exists. So you guys Indy third quarter. So this is religion. And let's say that this point Mississippi coordinates X comma. What? So with the given condition, we have and Tita equals school for Valtteri, which is equal school by my ex. So from here we can say that the value all so the value of X will be equal to minus three because in part quadrant, the X coordinate this negative similarly divide coordinated V equals two minus poor because in tar Corden by coroner, this negative now we can tell cleared the value of our allies equals to undergo X crept. Thus, vice, which implies R is equal school under about nine less 16 which implies our physical school fight. Now we can let the five predominate conscience so forced a sign which is equal school. Why, I and that is equals to minus four. But But then we have cost Tita, given that X upon which is equals to minus three van fight. Then we have got sick pita given. But out of one by that is equal to minus hi. It by who? Then? We have sex. Feta voyages equals who are upon X and that would be equals two minus fight by three. And the lasted number two Consciousness court puta, which is equal school it's upon by on that leak was three.


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