Can anybody help me with this equation? I am staring to think there is a mistake there....

I tried to factor it, but it does not seem right...

2sin^2(x) - 6sin(x)- 3=0

Printable View

- Jul 17th 2010, 02:04 PMAngie80Trigonometric equation
Can anybody help me with this equation? I am staring to think there is a mistake there....

I tried to factor it, but it does not seem right...

2sin^2(x) - 6sin(x)- 3=0 - Jul 17th 2010, 02:11 PMAlso sprach Zarathustra
Hint:

Quadratic equation. - Jul 17th 2010, 02:23 PMe^(i*pi)
Hint 2:

$\displaystyle |sin(x)| \leq 1$ - Jul 17th 2010, 02:36 PMAngie80
This is what I tried:

sinx=t

2t^2-6t-3=o

I used quadratic formula, and got:

t= ( 3- √15) /2 = -0.43

What now? I could substitute t for sinx now, but it does not help... - Jul 17th 2010, 03:18 PMmr fantastic
Exact solutions:

Let $\displaystyle x_1 = \frac{3 - \sqrt{15}}{2}$. Then $\displaystyle \sin (x) = x_1 \Rightarrow x = \sin^{-1} (x_1) + 2 n \pi$ or $\displaystyle x = \sin^{-1} (-x_1) + \pi + 2 n \pi$ (using the symmetry of the unit circle) where n is an integer.

Approximate solutions:

Use a calculator to get a decimal approximation of $\displaystyle \sin^{-1} \left( \frac{3 - \sqrt{15}}{2} \right)$ and then proceed in the usual way. - Jul 17th 2010, 03:50 PMAngie80
So, I calculated it and got appx: -26

I must be missing something, because I really do not know how to proceed from here... :(

I know how to use unit circle, but what is value of x, when sinx=-26??

I am veeery confused now.... - Jul 17th 2010, 05:49 PMmr fantastic
- Jul 17th 2010, 05:52 PMAngie80
Thanks soooo much!