A q about finiding a solution for a Trig. Function

**mHadad** · November 5th 2006, 10:09 AM

hi evreyone,
here is the q:

Find the solutions of the equation sin θ = 1/2 if:
(a) θ is in the interval [0, 2 pi )
(b) θ is any real number

**ThePerfectHacker** · November 5th 2006, 10:12 AM

Originally Posted by mHadad

hi evreyone,
here is the q:

Find the solutions of the equation sin θ = 1/2 if:
(a) θ is in the interval [0, 2 pi )
(b) θ is any real number

The solutions exist in the first and second quadrand because you are trying to find positive one.

The one in the first quadrand is $\pi/6$ then one in the second quadrand is, $\pi-\pi/6=5\pi/6$

**mHadad** · November 5th 2006, 10:28 AM

i have read in a solution for a q that sin θ = 2 has no solution, why?

**Quick** · November 5th 2006, 10:30 AM

Originally Posted by mHadad

i have read in a solution for a q that sin θ = 2 has no solution, why?

because $-1<\sin\theta<1$

**ThePerfectHacker** · November 5th 2006, 10:33 AM

Originally Posted by Quick

because $-1<\sin\theta<1$

Becuase,
$-1\leq \sin \theta \leq 1$

If you want to be cool

you can write,
$|\sin \theta|<1$

**Quick** · November 5th 2006, 12:03 PM

Originally Posted by ThePerfectHacker

Becuase,
$-1\leq \sin \theta \leq 1$

If you want to be cool

you can write,
$|\sin \theta|<1$

$|\sin \theta|\leq 1$

**CaptainBlack** · November 5th 2006, 12:05 PM

Originally Posted by mHadad

hi evreyone,
here is the q:

Find the solutions of the equation sin θ = 1/2 if:
(a) θ is in the interval [0, 2 pi )
(b) θ is any real number

If $\theta$ is a solution of $\sin(\theta)=1/2$ then so is $\theta_n = \theta+2\pi n, \ \ n=\pm 1, \ \pm 2, ...$ .

So using the solutions given by ImPerfectHacker we have:

$\pi/6+2 \pi n, n=0,\ \pm 1,\ \pm 2,\ ...$ , and $5 \pi/6+2 \pi n, n=0,\ \pm 1,\ \pm 2,\ ...$ comprise all the real solution.

RonL

**ThePerfectHacker** · November 5th 2006, 01:09 PM

Originally Posted by Quick

$|\sin \theta|\leq 1$

Wow, retard after a retard.

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