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mttal24

Member

Registered: 2012-05-01

Posts: 23

Trignometry: Question on a Trignometric equation

I know that a principal solution of a trignometric equation is 2 values lying between

But I don't know how to find them.
Lets take a question,
Find the principal solutions of

I know,

And, in some books I see that, suddenly out of the blues, a person adds

to

and makes it

I just know that values of sine and cos repeat after

Please give me full explanation on how to find this. Please explain with one more example so that it becomes clear to me :

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: Trignometry: Question on a Trignometric equation

hi

See pictures.

Because the tan function keeps repeating, you can get the same value for tan x every pi radians.

So if pi/3 is a solution, so is pi/3 + pi = 4pi/3

For sec 2

sec is 1/cos.

Cosine is +ve in the 1st quadrant (0, pi/2) and 4th quadrant (3pi/2, 2pi)

So once you have done inverse sec 2 and got the first angle, subtract from 2pi to get another.

http://www.mathsisfun.com/algebra/trig- … raphs.html

and

http://www.mathsisfun.com/algebra/trig- … rants.html

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

mttal24

Member

Registered: 2012-05-01

Posts: 23

Re: Trignometry: Question on a Trignometric equation

Thanks
And if

then how would you do since a -ve value means

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: Trignometry: Question on a Trignometric equation

Hi mttal24

-ve means negative and +ve positive.

---

“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: Trignometry: Question on a Trignometric equation

sec x = -2

=> 1/cos x = -2

=> cos x = -1/2

cosine is negative between pi/2 and 3pi/2

note also: cos x = +1/2 has a solution pi/3

So the solutions we want (in the 2nd and 3rd quadrant) are      pi - pi/3 = 2pi/3       and         pi + pi/3 = 4pi/3

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

mttal24

Member

Registered: 2012-05-01

Posts: 23

Re: Trignometry: Question on a Trignometric equation

Thanks.
Lets say, I begin answering by:

Now, I know sec/cos is negative between

implies,

But, here we are taught by a different method where we see that the main identities that,

Similarly,

I tried understanding this in many books, which I wrote as

And, in some books I see that, suddenly out of the blues, a person adds

to

and makes it

Now, I have understood that after reading the same question for the past 5 days.
But your method seems to be faster.

Last edited by mttal24 (2012-05-13 20:19:27)