1. ## Equation solutions

I want to find x-axis intercepts of this equation:
(sin x+0.5)(sin x-0.25)=0.25

0 <= x <= 360.

So sin x=-0.25 or sin x=0.5

One of the associated acute angles is 30 which is found from sin x=0.5. The other is 48.59 but I don't know where it comes from.

2. hi
put $\sin x=X$
and solve $(X+0.5)(X-0.25)-0.25=0$

3. I rearranged the equation to equal 0 using +.75 and -.5. I then solved the problem but I don't know why I couldn't solve it with the other equation.

4. I think it must be necessary to factorise without any added on value. Completing the square for instance wouldn't work.

5. Originally Posted by Stuck Man
I think it must be necessary to factorise without any added on value. Completing the square for instance wouldn't work.

to find the x-intercepts you must solve the given equation,

$(X+0.5)(X-0.25)-0.25=X^2-0.25X+0.5X-0.375=X^2+0.25X-0.375=0$.
i found the solutions $0.5$ and $-0.75$
therefore,
$\sin x=0.50 \Leftrightarrow x=\arcsin (0.50)$
or
$\sin x=-0.75\Leftrightarrow x=\arcsin (-0.75)$.

6. I think you've mixed up the signs of the solutions. You've rewritten the formula the same as I did. I'm still not sure why I have to fully factorise and not use the Completing The square method. I think it have something to do with the use of sin.

7. Originally Posted by Stuck Man
I want to find x-axis intercepts of this equation:
(sin x+0.5)(sin x-0.25)=0.25

0 <= x <= 360.

So sin x=-0.25 or sin x=0.5

One of the associated acute angles is 30 which is found from sin x=0.5. The other is 48.59 but I don't know where it comes from.
$\sin^2{x} + .25\sin{x} - 0.125 = 0.25
$

$\sin^2{x} + .25\sin{x} - 0.375 = 0$

$8\sin^2{x} + 2\sin{x} - 3 = 0$

$(4\sin{x} + 3)(2\sin{x} - 1) = 0$

$\sin{x} = \frac{3}{4}$ ...

$x = \arcsin\left(\frac{3}{4}\right) \approx 48.59^\circ$

$x = 180 - \arcsin\left(\frac{3}{4}\right) \approx 131.4^\circ$

$\sin{x} = \frac{1}{2}$

$x = 30^\circ$

$x = 150^\circ$

8. I still don't know why I can't use the equation as it was originally:
(sin x+0.5)(sin x-0.25)=0.25

sin x=-0.25 or sin x=0.5

9. Originally Posted by Stuck Man
I still don't know why I can't use the equation as it was originally:
(sin x+0.5)(sin x-0.25)=0.25

sin x=-0.25 or sin x=0.5
You can't do that in math.

Now if the equation was

$(\sin{x}+.5)(\sin{x}-.25) = 0$

then you could do that

Notice how Raoh and Skeeter set the equation equal to 0 and then solved.