Question 817300: Please help me solve this equation:
2*sin(x+(3pi/2))+1 = 0
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! problem is:
2 * sin(x + 3pi/2) + 1 = 0
subtract 1 from both sides of this equation to get:
2 * sin(x + 3pi/2) = -1
divide both sides of this equation by 2 to get:
sin(x + 3pi/2) = -1/2
3pi/2 converted to degrees is equal to 3pi/2 * 180/pi which is equal to 3(180)/2 which is equal to 3(90) which is equal to 270.
your equation becomes:
sin(x + 270) = -1/2
to find (x + 270), you need to find sin^-1(-1/2)
sin(1/2) is equal to 30 degrees.
when the sin is negative the angle can be in the third or fourth quadrant.
third quadrant would be 180 + 30 = 210 degrees.
fourth quadrant would be 360 - 30 = 330 degrees.
so there are 2 possible solutions.
x + 270 = 210 degrees.
x + 270 = 330 degrees.
this means that:
x = 210 - 270 = -60 degrees, or:
x = 330 - 270 = 60 degrees.
let's see if that's right.
your equation is, after converting 3pi/2 to degrees:
2*sin(x + 270) + 1 = 0
we determined that x = either 60 degrees or -60 degrees.
assume x = -60 degrees.
equation becomes:
2 * sin(-60 + 270) + 1 = 0 which simplifies to:
2 * sin(210) + 1 = 0
use your calculator to find that sin(210)= -.5
substitute -.5 for sin(210) and your equation becomes:
2 * -.5 + 1 = 0 which becomes:
-1 + 1 = 0 which becomes:
0 = 0, confirming that x = -60 degrees is a solution to the original equation.
now assume x = 60 degrees.
equation becomes:
2 * sin(60 + 270) + 1 = 0 which becomes:
2 * sin(330) + 1 = 0
use your calculator to find that sin(330) = -.5
substitute -.5 for sin(330) and your equation becomes:
2 * -.5 + 1 = 0 which becomes:
-1 + 1 = 0 which becomes:
0 = 0, confirming that x = 60 degrees is also a solution to the original equation.
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