Inverse trigonometric functions

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November 18th 2008, 07:50 AM
iceman1

Inverse trigonometric functions

Hello ,

solve cosx = 2/7 for x [Pie , 2Pie]

My solution is first : Arc cos ==> 1.28 rd , 1.28/3.14 = 0.4076 Pie its not in the domain so what to do ? (Thinking) I don't know what to do after that ? please can you help me ?

Thanks
November 18th 2008, 08:17 AM
Soroban

Hello, iceman1!

By the way, it's not "pie" . . . it's "pi".

Quote:

Solve: . $\cos x \:=\:\tfrac{2}{7}\quad\text{for }[\pi,\:2\pi]$

My solution is first: . $\arccos\left(\tfrac{2}{7}\right) \:=\:1.28\text{ rd} \quad\Rightarrow\quad \frac{1.28}{\pi}$ . ?? . Why?

An inverse trig function has an infinite number of values.

. . $\arccos\left(\tfrac{2}{7}\right) \;=\;\pm1.281 + 2\pi n\;\;\text{ for any integer }n$

Now find $n$ so that the angle falls within the interval.
November 18th 2008, 08:27 AM
iceman1

oh thanks yeah sorry ''PI'' . 1.28/pi to get the result is PI ? coz its in Radian .

anway how to find n ? (Itwasntme) I need an exemple how to resolve this problem .

our teacher is drawing the circle and i m lost sometimes she adjust -Pi -x , +Pi + x (Worried) Please can you help me how to know ?

Thanks (Rock)
November 18th 2008, 11:22 AM
HallsofIvy

Quote:

Originally Posted by iceman1

oh thanks yeah sorry ''PI'' . 1.28/pi to get the result is PI ? coz its in Radian .

anway how to find n ? (Itwasntme) I need an exemple how to resolve this problem .

our teacher is drawing the circle and i m lost sometimes she adjust -Pi -x , +Pi + x (Worried) Please can you help me how to know ?

Thanks (Rock)

Soroban told you that " $<br /> \arccos\left(\tfrac{2}{7}\right) \;=\;\pm1.281 + 2\pi n\;\;\text{ for any integer }n<br />$
When n is 0, that is 1.281 radians. When n= 1, that is 1.281+ 2(3.141)= 7.563 and 1.281- 2(3.141)= -5.002. When n= 2, ... Do the arithmetic!