SOLUTION: i need an example of how to go about working out the solutions of an equation
for e.g. Sinx= 0.5 with the domain XE[0,pi]
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for e.g. Sinx= 0.5 with the domain XE[0,pi]
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Question 875459: i need an example of how to go about working out the solutions of an equation
for e.g. Sinx= 0.5 with the domain XE[0,pi] Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website! here's a graph of the sine function.
the horizontal line is at y = .5
the first vertical line is at x = pi/6.
the second vertical line is at x = 5pi/6.
the third vertical line is at x = pi.
what this is showing you is that your solution is at x = pi/6 and x = 5pi/6.
both of those values of x are in the interval from x = 0 to x = pi.
you can convert your radians to degrees by multiplying the radians by 180/pi.
pi/6 * 180/pi = 180/6 = 30 degrees.
5pi/6 * 180/pi = 5*6/180 = 5*30 = 150 degrees.
pi * 180 / pi = 180 degrees.
you should be able to find sin(x) in quadrant 1.
sin(x) = .5 gets you x = arcsin(.5) = 30 degrees or pi/6 radians.
your calculator will show pi/6 radians as .5235987756
it doesn't matter.
you can still convert it to degrees by multiplying by 180/pi.
.5235987756 * 180/pi = 30 degrees.
working in degrees is sometimes easier.
your interval of 0 to pi is equivalent to an interval from 0 degrees to 180 degrees.
sin(30) = .5
that's in quadrant 1.
the interval spans quadrant 1 and quadrant 2.
the equivalent angle in quadrant 2 would be 180 - 30 which would be equal to 150 degrees.
the sin of 150 degrees is equal to the sine of 30 degrees in quadrant 2 which is equal to .5.
here's a reference on reference angles that might help:
