Trig equations: find solutions of 3sin^2x-sinx-2=0 in the interval [-pi,pi]. what does the interval mean?! I know how to do the equation part. when you do the equation, it becomes (sinx-1)(3sinx+2)=0, with the answers of x=pi/2 and in Q3:-2.41 and in Q4: x=-0.730. i can do it just what does "interval" mean?

Question

zehanz · Answer

It means your solutions have to be numbers between -pi and pi.
You've found that x=pi/2 will do the job, and it satisfies this condition.
But, 2.5pi, or 4.5pi would also be a solution of the equation, because for these numbers also: sinx -1 = 0. 
Still, these numbers are not allowed, because of the [-pi,pi] restriction.

anonymous · Answer

oh so it just means that, if a graph x scale was labeled by let's say intervals of pi, the lowest the number on the x possible would be -pi and biggest number pi?

zehanz · Answer

Yes, that is right!

In short, because of the repetitive nature of the sine function, there are often an infinity of numbers that are solutions of equations involving sines. By restricting the solutions to certain intervals, such as [-pi,pi] you have to check whether a solution satisfies this condition or not. It is just an extra step you have to take!

anonymous · Answer

ohh i see. thanks!

zehanz · Answer

YW!