Solve Each Of These, giving solutions between 0 and 2Pie in terms of Pie?

Question

a) sinX = 1/2

b) sinX = 1

Please can you explain to me how to do this aswell, I also have the answers to these, but do not know how to get there. The answers are:
a) Pie/6 , 5pie/6
b) pie/2

Any help would be apreciated

oh yeah lol, yeah im on about Pi, im just hungry thats all. : {)

Answer 1

Boy, it's "Pi", not PIE!

a) x = pi/6 and x = 5pi/6

one way to solve this is to type sin^(-1)[1/2] into your calculator and you get the answer pi/6 (or 30 deg). But you should really know by heart the values of sin/cos of 0,pi/6, pi/4, pi/3, pi/2, pi and 2pi.
Then sketch a graph of sinx between 0 and 2 pi . draw a horizontal line at y=1/2. You'll see that the line cuts the sin curve in 2 places. The first one is pi/6 (you already know that by now) and you only need to work out the other one.
The graph between 0 and Pi is symmetrical. It has a shape of a "hill". the first solution is Pi/6 to the right from the left side of the hill. therefore the other soution must be Pi/6 to the left from the right end of the hill, i.e.
Pi - Pi/6 = 5Pi/6


b) sin x = 1... you should really know by heart that sin hits 1 at Pi/2. If you don't use your calculator and epeat the process described above.


I guess you might have troubles using your calculator as it probably displays Pi as 3.141592654.... and it is not easy to see that 0.523598775 is really Pi/6. So you really need to learn the table of the basic values of sin and cos.

Hope this helps.

Answer 2

If sinx = 1/2 x= pi/6 in the first cuadrant but also its symmetric in the second cuadrant has the same si and that angle would be pi-pi/6=
=5p/6. If sinx = 1 the only angle (0,2pi) is x= pi/2

Answer 3

I can get the answers from doing sin^-1 of 1/2 and 1 on a calculator

then you know that there are two values for sin x = 30 within 360 degrees. (look up cast graphs) for the second one only sin 90 gives positive 1.