My Math Forum  

Go Back   My Math Forum > High School Math Forum > Trigonometry

Trigonometry Trigonometry Math Forum


Reply
 
LinkBack Thread Tools Display Modes
September 26th, 2014, 05:22 AM   #1
Newbie
 
Joined: Sep 2014
From: Somewhere

Posts: 3
Thanks: 0

Unhappy 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.
Centaur is offline  
 
September 26th, 2014, 05:40 AM   #2
Math Team
 
Joined: Dec 2013
From: Colombia

Posts: 7,344
Thanks: 2466

Math Focus: Mainly analysis and algebra
Perhaps you were supposed to use $$1 + \cot^2 x = \csc^2 x$$
v8archie is offline  
September 26th, 2014, 09:27 AM   #3
Newbie
 
Joined: Sep 2014
From: Somewhere

Posts: 3
Thanks: 0

Quote:
Originally Posted by v8archie View Post
Perhaps you were supposed to use $$1 + \cot^2 x = \csc^2 x$$
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.
Centaur is offline  
September 27th, 2014, 09:07 AM   #4
Global Moderator
 
Joined: Dec 2006

Posts: 19,297
Thanks: 1687

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.
skipjack is offline  
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
mac_alleb is offline  
October 1st, 2014, 08:34 AM   #6
Senior Member
 
Joined: Jul 2014
From: भारत

Posts: 1,178
Thanks: 230

Quote:
Originally Posted by mac_alleb View Post
Another question of a kind:
Define Sin without right triangle
the measurement of one of the non-right 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.
Prakhar is offline  
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)???
mac_alleb is offline  
October 1st, 2014, 04:40 PM   #8
Global Moderator
 
Joined: Dec 2006

Posts: 19,297
Thanks: 1687

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.
skipjack is offline  
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.
Centaur is offline  
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.
Polyhymnio is offline  
Reply

  My Math Forum > High School Math Forum > Trigonometry

Tags
basic, confusing, easy, trig



Search tags for this page
Click on a term to search for related topics.
Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Graphing calculator apps for easy trig? jonatron5 Math Software 4 February 1st, 2016 08:48 PM
Easy trig question dmxnemesis Algebra 3 December 2nd, 2010 04:40 PM
Help with four basic/easy integrals... golfman44 Calculus 1 December 4th, 2009 02:34 AM
Confusing trig problem need help suomik1988 Algebra 4 October 28th, 2009 01:27 AM
Fairly Basic/Easy Probablity Problem? eysikal Algebra 6 July 28th, 2009 10:11 PM





Copyright © 2018 My Math Forum. All rights reserved.