How many solutions in 4sin2x=3?

**MaddieMoodle** · February 21st 2013, 11:30 AM

Hello guys,
I am just wandering how many solution there are to the equation in the title?
The boundary is 0_<X_<360(degrees) (_< meaning less than or equal to sign)

I worked out:
sin2x=0.75
2x=sin^-1(0.75)
2x=48.9^o
x=48.9x0.5
x= 24.3

I know this is one solution, but is there any more solutions to this?

Thanks
Maddie

**zhandele** · February 21st 2013, 01:25 PM

I believe there are four solutions in this range. An easy way to see this is to graph them. See the attached pdf.

Do you know how to find the other solutions?

**Prove It** · February 21st 2013, 10:01 PM

Originally Posted by MaddieMoodle

Hello guys,
I am just wandering how many solution there are to the equation in the title?
The boundary is 0_<X_<360(degrees) (_< meaning less than or equal to sign)

I worked out:
sin2x=0.75
2x=sin^-1(0.75)
2x=48.9^o
x=48.9x0.5
x= 24.3

I know this is one solution, but is there any more solutions to this?

Thanks
Maddie

The period of this function is $\displaystyle \begin{align*} 180^{\circ} \end{align*}$ , and there are two solutions for each period.

**MINOANMAN** · February 21st 2013, 10:31 PM

There are 4 solutions
24.3 , 204.3 , 65.7 and 245.7

**astartleddeer** · February 22nd 2013, 03:00 PM

$0 \leq x \leq 360^{o} \Rightarrow 0 \leq 2x \leq 720^{o}$

$sin(2x) = \frac{3}{4}$

$2x = Arcsin(\frac{3}{4})$

$2x = 360^{o} + Arcsin(\frac{3}{4})$

$2x = 180^{o} - Arcsin(\frac{3}{4})$

$2x = 540^{o} - Arcsin(\frac{3}{4})$

$\Rightarrow$

$x = \frac{Arcsin(\frac{3}{4})}{2} \approx 24.3^o$

$x = \frac{180^{o} - Arcsin(\frac{3}{4})}{2} \approx 65.7^o$

$x = \frac{360^{o} + Arcsin(\frac{3}{4})}{2} \approx 204.3^o$

$x = \frac{540^{o} - Arcsin(\frac{3}{4})}{2} \approx 245.7^o$

Thread: How many solutions in 4sin2x=3?

LinkBack

Thread Tools

Display

How many solutions in 4sin2x=3?

Re: How many solutions in 4sin2x=3?

Re: How many solutions in 4sin2x=3?

Re: How many solutions in 4sin2x=3?

Re: How many solutions in 4sin2x=3?

Similar Math Help Forum Discussions

Too Many Solutions: tan x = 3 sin x

Infinitely many solutions (Edit: No solutions)

For which values of k are there no solutions, 1 solution, inifinite solutions.

solutions..

sum of solutions?

Search Tags