For a) is the answer 157.5 degrees? And do they want it in degrees or would I have to put it into radian form?
For b) I need help with. Would the answer be 122.7 degrees?
Thank you so much!
Leave it in radians and in terms of $\displaystyle \pi$. With these questions always leave it in the units which the question is given in. For all but the most basic trig you'll be using radians anyway
As you can gather from the graph $\displaystyle y = \sin(x)$ is symmetrical in the line $\displaystyle x = \frac{\pi}{2}$
This means that the distance between $\displaystyle x = \frac{\pi}{2}$ and $\displaystyle x=A$ is equal to the distance between $\displaystyle x = \frac{\pi}{2}$ and $\displaystyle x=B$
Hence $\displaystyle B = \frac{\pi}{2} + \left(\frac{\pi}{2} - A\right)$ which should be $\displaystyle B = \frac{7\pi}{8} $ (which is roughly 157.5 degrees)
For part b use the same principle to get $\displaystyle B = \pi - 1$ which is a perfectly acceptable answer and again the same answer you got
Thank you so much for helping me with this problem!
Also since we are still on the subject, how would I solve this problem?
I know that;
3pi/2 = -1
pi = 0
pi/2 = 1
However what do I do with the other values they gave me such as 1,2,4,5?
Do I convert them into degrees first and then take the sign of it? For example 1 is 1(180)/pi = sin 180/pi = 0.6495? Or how would I solve this kind of a problem?
Leave them in radians.
EDIT: Also your method does work (long winded though since all scientific calculators worthy of the name have a radians mode so you can find $\displaystyle \sin(1)$ directly using radian mode) it is a long way around when you can do it mentally using local maxima and minima (which sounds far more complicated than it is!)
As you've mentioned on this graph $\displaystyle \frac{\pi}{2} = 1$ and $\displaystyle \frac{3\pi}{2} = -1$ and $\displaystyle \pi = 0$
We know that $\displaystyle \pi \approx 3.14$. This means if you evaluate $\displaystyle \frac{\pi}{2}$ and use a decimal approximation you will notice that $\displaystyle 1 < \frac{\pi}{2} < 2 < \pi$ and so you can place 1 and 2.
It is same procedure for finding 4 and 5