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September 26th, 2014, 05:22 AM  #1 
Newbie Joined: Sep 2014 From: Somewhere Posts: 3 Thanks: 0  Basic and easy trig! This has been confusing me
This has been confusing me, and my teacher isn't giving me an answer idk why. I had a quiz 2 weeks ago and there was a right triangle and the question said that I'm supposed to use csc to find a missing angle. And these were the only values that were given: The right triangle sign obviously the value of the opposite side the value of the adjacent side So this is how I found the value of the missing angle: 1) I used Pythagorean theorem to find the value of the hyp 2) I used csc (1/sin=h/o) and found the angle the angle was about 54 degrees and the teacher corrected it and said that my answer is correct. so here are my questions. BTW I've asked this like 2 times now and people still keep on giving me very complex answers! I just started trig please give me VERY simple answers! 1) As far as I know, we should use inverse trig functions to find MISSING ANGLES! So why didn't the question say "Find the missing angle using arccsc"??? Why did we use csc? 2) Since inverse trig functions are used to find missing angles why do we in class use the regular 6 trig functions such as sin, csc, tan etc... to find the angle? 3) Is it actually possible to use the 6 trig functions to find angles? 4) I read that inverses should be used to find an angle when ONLY 2 sides of the triangle are given but we can clearly use the pyth. theorem to find the missing side in a right triangle so why should I use an inverse if I can find the side? BTW WE ARE WORKING ON RIGHT ANGLE TRIG RIGHT NOW and I just started this class so please make your answers as simple as possible! Thanks Last edited by skipjack; September 27th, 2014 at 08:01 AM. 
September 26th, 2014, 05:40 AM  #2 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,659 Thanks: 2635 Math Focus: Mainly analysis and algebra 
Perhaps you were supposed to use $$1 + \cot^2 x = \csc^2 x$$

September 26th, 2014, 09:27 AM  #3 
Newbie Joined: Sep 2014 From: Somewhere Posts: 3 Thanks: 0  Nope, we have not taken this. As I have told you, my answer was correct (I think?) But it made me very confused (read the questions I listed).
Last edited by skipjack; September 27th, 2014 at 08:02 AM. 
September 27th, 2014, 09:07 AM  #4 
Global Moderator Joined: Dec 2006 Posts: 20,641 Thanks: 2083 
Suppose the opposite and adjacent sides are of length 1 and √3 respectively, so that the hypotenuse has length 2. If θ is the angle between the hypotenuse and the side of length √3, csc(θ) = 2. That implies that θ = arccsc(2) = 30°. In the above, I first wrote an equation that involved csc, then I used arccsc to solve that equation. In a sense, I "used" both functions. As I happen to know that csc(30°) = 2, I could have deduced directly that θ = 30°. However, such knowledge is equivalent to knowing that arccsc(2) = 30°, so I would still implicitly have been using arccsc. If you know the formula θ = arccsc(hyp/opp), you can proceed similarly, but without having to involve the csc function. One can sometimes find an angle without use of any inverse trigonometric function (even implicit use). For example, each angle of an equilateral triangle must be 60° because the three angles are the same and must total 180°. In general, though, you would need to use an inverse trigonometric function. I think the wording of the question was a bit unusual. It was presumably because a particular method was wanted. If any method of solution had been allowed, you could have used the arctan function, and this would have been simpler than calculating the hypotenuse and then using arccsc. In general, you can't use just the six trigonometric functions to find an angle. However, once you know two angles of a triangle, you can, of course, calculate the third angle without further use of trigonometry. Last edited by skipjack; October 10th, 2014 at 05:55 AM. 
October 1st, 2014, 07:36 AM  #5 
Newbie Joined: Jan 2014 Posts: 14 Thanks: 0 
Another question of a kind: Define Sin without right triangle 
October 1st, 2014, 08:34 AM  #6 
Senior Member Joined: Jul 2014 From: भारत Posts: 1,178 Thanks: 230  the measurement of one of the nonright angles (q) the length of the side adjacent to that angle. the length of the triangle's hypotenuse. Futhermore, Definition I gives exact equations that describe each of these relations: sin(q) = opposite / hypotenuse. 
October 1st, 2014, 09:26 AM  #7 
Newbie Joined: Jan 2014 Posts: 14 Thanks: 0 
Arctan as well as all trig functions possibly has defs throw rows and polynomial. But the very question is How to connect it with triangle def. More future Sin := f(x,y)??? 
October 1st, 2014, 04:40 PM  #8 
Global Moderator Joined: Dec 2006 Posts: 20,641 Thanks: 2083 
One could define sin(A) as a/d, where d is the diameter of the circumcircle of the triangle ABC with side of length a opposite angle A.

October 9th, 2014, 06:11 AM  #9 
Newbie Joined: Sep 2014 From: Somewhere Posts: 3 Thanks: 0 
Thanks for the explanation Your efforts are highly appreciated.

October 13th, 2014, 02:45 PM  #10 
Newbie Joined: Oct 2014 From: Ohio Posts: 9 Thanks: 4 
You have to use the inverse trig functions to find angles. You have not properly understood what your teacher was doing in class.
Last edited by skipjack; October 13th, 2014 at 08:25 PM. 

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