Question 1183228: Find all solutions to 2sin(0)=sqrt(3) on the interval 0≤0<2π
0=
Give answers as exact values, as a list separated by commas
I'm really confused with this question. can someone show me in detail how to tackle this problem, thank you.
Found 2 solutions by MathLover1, Theo:
Answer by MathLover1(20850)   (Show Source):
Answer by Theo(13342)  (Show Source):
You can put this solution on YOUR website! let x = theta.
the equation becomes 2 * sin(x) = sqrt(3).
divide both sides of the equation by 2 to get:
sin(x) = sqrt(3)/2
use your calculator to find arcsin(sqrt3)/2) = 60 degrees when you calculator is set to degrees and not radians.
that's the angle in the first quadrant.
since sine is positive in first and second quadrant, then the equivalent angle in the second quadrant is 180 - 60 = 120 degrees.
since sine is negative in the third and fourth quadrants, your angle will be in the first and second wuadrants only.
convert your angle to radians to get:
60 degrees * pi / 180 = pi/3 radians.
120 degrees * pi/180 = 3pi/3 radians.
on a graph, this looks like this.
to graph the solution, you break up 2 * sin(x) = sqrt(3) into two equations.
they will be y = 2 * sin(x) and y = sqrt(3).
the intersection of those two equations is your solution.
note that sqrt(3) = 1.732050808 which is equal to 1.732 when rounded to 3 decimal places, as shown on the graph.
the same graph, in degrees, is shown below.
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