Which equation is correct for this sinusoid?
And why?
The question doesn't really make sense. For example, take A.
We have:
$\displaystyle 2\sin{x}-1=0$
$\displaystyle 2\sin{x}=1$
$\displaystyle \sin{x}=\frac{1}{2}$
Which is solvable for $\displaystyle x$, and doesn't really represent any of the graphs.
However, you can work out which of those possible graphs could give these solutions - just solve each equation in turn for x and see which one gives the required intercepts.
Very bad choices. What's the amplitude of y = 2*cos(x) of y = 2*sin(x)?
It appears we have y = sin(x), without any alteration.
Perhaps the snie wave shown above is for reference only and this is really a four-part question. You must build the others!
Just guessing.
It would help if you posted the actual question exactly as written in the textbook. From the multiple choice options, I can guess that the actual question was something like "Which of the following equations gives the x-coordinates of the intersection points shown" or something similar.
You have y = sin(x) and y = 0.5. Now use what you know about solving simultaneous equations. If you need more help, please show all the effort you have made.
This question doesn't make sense for 2 reasons:
A) I'm 99.9% positive that graph is for y=sin(x). For this equation y=1/2 at 30 and 150 degrees. $\displaystyle \frac{\pi}{6}$ and $\displaystyle \frac{5\pi}{6}$ Which seems about right. However, its hard to tell the amplitude without y being labeled other than at 0.5
B) if you give a specific value like: 2sin(x)-1 = 0. You won't get a continuous graph. You will get a set of 2 points. Specifically for this one at :
$\displaystyle (\frac{\pi}{6},0)$ and $\displaystyle (\frac{5\pi}{6},0)$
This will be true of all 4 equations.