Math Is Fun Forum
You are not logged in.
- Topics: Active | Unanswered
Pages: 1
#1 2018-01-29 03:27:41
- Monox D. I-Fly
- Member
- From: Indonesia
- Registered: 2015-12-02
- Posts: 2,000
[ASK] Trigonometric Equation
If 0 < x < 90, what is the solution of tan(2x - 5) = cot(x + 5)?
I got stuck in tan(2x - 5)tan(x + 5) = 1. What should I do after that?
Actually I never watch Star Wars and not interested in it anyway, but I choose a Yoda card as my avatar in honor of our great friend bobbym who has passed away.
May his adventurous soul rest in peace at heaven.
Offline
#2 2018-01-29 03:39:45
- Alg Num Theory
- Member
- Registered: 2017-11-24
- Posts: 693
- Website
Re: [ASK] Trigonometric Equation
Oops, that does not work. If tanAtanB = 1, then the denominator in the formula for tan(A+B) is 0.
Sorry, back to the drawing board …
Last edited by Alg Num Theory (2018-01-29 03:45:41)
Me, or the ugly man, whatever (3,3,6)
Offline
#3 2018-01-29 04:43:53
- Bob
- Administrator
- Registered: 2010-06-20
- Posts: 10,640
Re: [ASK] Trigonometric Equation
try using:
cos(A-B) + cos(A+B) = 2 cos(A) . cos(B)
A = 2x-5 and B = x+5
and a similar formula with a minus sign.
Bob
Children are not defined by school ...........The Fonz
You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you! …………….Bob 
Offline
#4 2018-01-29 12:44:27
- Monox D. I-Fly
- Member
- From: Indonesia
- Registered: 2015-12-02
- Posts: 2,000
Re: [ASK] Trigonometric Equation
What does it have to do with cos? The questions are tan and cot.
Actually I never watch Star Wars and not interested in it anyway, but I choose a Yoda card as my avatar in honor of our great friend bobbym who has passed away.
May his adventurous soul rest in peace at heaven.
Offline
#5 2018-01-29 20:45:53
- Bob
- Administrator
- Registered: 2010-06-20
- Posts: 10,640
Re: [ASK] Trigonometric Equation
hi Monox D. I-Fly
Sorry my post was too brief. I was in a hurry as I had to go out. Here's some more detail:
note:
Let A = 2x-5 and B = x+5 => A-B = x - 10 and A+B = 3x
The two trig. formulas that will help are
and
so the equation becomes:
I'll leave you to finish this.
Bob
Children are not defined by school ...........The Fonz
You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you! …………….Bob
Offline
#6 2018-01-30 03:23:56
- Alg Num Theory
- Member
- Registered: 2017-11-24
- Posts: 693
- Website
Re: [ASK] Trigonometric Equation
I have an idea: if tanA·tanB = 1, then A+B must be an odd multiple of 90°. Example:
[list=*]
[*]
[/list]
and 30° + 60° = 90°.
In the OP’s example, 0 < x < 90°, so 0 < (2x + 5) + (x − 5) = 3x < 270° ⇒ x = 90°.
PS: Check: tan(175°) = 1/tan(95°) so I think I’m on the right track.
Last edited by Alg Num Theory (2018-01-30 03:27:23)
Me, or the ugly man, whatever (3,3,6)
Offline
#7 2018-01-30 14:24:40
- Monox D. I-Fly
- Member
- From: Indonesia
- Registered: 2015-12-02
- Posts: 2,000
Re: [ASK] Trigonometric Equation
Huh? You got 90°? What I got was 30°.
Actually I never watch Star Wars and not interested in it anyway, but I choose a Yoda card as my avatar in honor of our great friend bobbym who has passed away.
May his adventurous soul rest in peace at heaven.
Offline
#8 2018-01-30 16:20:57
- Alg Num Theory
- Member
- Registered: 2017-11-24
- Posts: 693
- Website
Re: [ASK] Trigonometric Equation
Sorry, I meant to say 3x = 90°, so yes, x = 30°.
Me, or the ugly man, whatever (3,3,6)
Offline
Pages: 1