Trigonometric equations
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Trigonometric equations
(OT: nobody's posting lately...)
i've been having a hard time with solving trigonometric equations... can anyone help me to understand better on how to solve this 3 = = \ /'/ 6 stuff...
thanks!
i've been having a hard time with solving trigonometric equations... can anyone help me to understand better on how to solve this 3 = = \ /'/ 6 stuff...
thanks!
schmaltzy Level 4

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Re: Trigonometric equations
Wait, trigonometric EQUATIONS or IDENTITIES?
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hmm00 Admin
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Re: Trigonometric equations
equations...
schmaltzy Level 4

Number of posts : 64
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Re: Trigonometric equations
OK then. *looks for trigonometry book*
Okay...
Here we go...
SOURCE: Plane and Spherical Trigonometry, Paul Rider
Before you can answer trigonometric equations, you need to know, if not master, the trigonometric identities.
Actually, there are two kinds of equations. One is the Identical Equation, or simply identity. The other is the Conditional Equation. The difference between the two? Identical equations are those which are satisfied by all values (with some exceptions), while conditional equations are satisfied be certain values only.
So, I'll be discussing the conditional equations here.
"There is no general method of solving trigonometic equations. If the equation contains a single function of an angle, solve for this function by appropriate algebraic methods, and then find the corresponding values of the angle. If more than one function appears in the equation, the equation should ordinarily be transformed so that it contains only one function, or into factored form so that each factor contains only one function." pg.178
so let's take similar examples from the book (pg.181)
#3.) tanA cotA = 2
we know that cotA = 1/tanA
tanA + (1/tanA) = 2
(tan2A + 1)/tanA = 2 ___ cross multiply
tan2A + 1 = 2tanA
tan2A  2tanA + 1 = 0 ___ factor
(tanA  1)(tanA  1) = 0 ___ equate to 0
tanA  1 = 0; tanA  1 = 0
tanA = 1; tanA = 1 ___ from here you start using your calculator, or you could use special triangles/angles. You can actually analyse from here. In this case, the tangent of what angle is equal to 1?
A = arctan 1; A = arctan 1
A = 45; A = 45
(i'll update this later...or if this is enough just tell me. BTW how urgent is this?)
Okay...
Here we go...
SOURCE: Plane and Spherical Trigonometry, Paul Rider
Before you can answer trigonometric equations, you need to know, if not master, the trigonometric identities.
Actually, there are two kinds of equations. One is the Identical Equation, or simply identity. The other is the Conditional Equation. The difference between the two? Identical equations are those which are satisfied by all values (with some exceptions), while conditional equations are satisfied be certain values only.
So, I'll be discussing the conditional equations here.
"There is no general method of solving trigonometic equations. If the equation contains a single function of an angle, solve for this function by appropriate algebraic methods, and then find the corresponding values of the angle. If more than one function appears in the equation, the equation should ordinarily be transformed so that it contains only one function, or into factored form so that each factor contains only one function." pg.178
so let's take similar examples from the book (pg.181)
#3.) tanA cotA = 2
we know that cotA = 1/tanA
tanA + (1/tanA) = 2
(tan2A + 1)/tanA = 2 ___ cross multiply
tan2A + 1 = 2tanA
tan2A  2tanA + 1 = 0 ___ factor
(tanA  1)(tanA  1) = 0 ___ equate to 0
tanA  1 = 0; tanA  1 = 0
tanA = 1; tanA = 1 ___ from here you start using your calculator, or you could use special triangles/angles. You can actually analyse from here. In this case, the tangent of what angle is equal to 1?
A = arctan 1; A = arctan 1
A = 45; A = 45
(i'll update this later...or if this is enough just tell me. BTW how urgent is this?)
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hmm00 Admin
 Number of posts : 187
Age : 27
Location : Baguio po!
Registration date : 20071008
Re: Trigonometric equations
the example makes things clearer.. haha...
yes that's just enough... and it's not really urgent... i just really wanted to make things uhmmm.... clearer....
i'm just really hard up with what identity i should choose to solve the equation...
thank you...!
yes that's just enough... and it's not really urgent... i just really wanted to make things uhmmm.... clearer....
i'm just really hard up with what identity i should choose to solve the equation...
thank you...!
schmaltzy Level 4

Number of posts : 64
Location : neverwhere
Job/hobbies : reading, sketching, eating, sleeping, music
Registration date : 20071015
Re: Trigonometric equations
You're welcome. Just post if you need more clarifications! I'd go to Shier... City High but I don't have the time to go there and I hate those security guards who actally do more annoyance than guarding
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hmm00 Admin
 Number of posts : 187
Age : 27
Location : Baguio po!
Registration date : 20071008
Re: Trigonometric equations
haahaa... shierr.... got that right... sigh...
schmaltzy Level 4

Number of posts : 64
Location : neverwhere
Job/hobbies : reading, sketching, eating, sleeping, music
Registration date : 20071015
Twilight :: Academics :: Mathematics :: Trigonometry
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