write the number of points of intersection of 2y=1 and y= sinx. -2pi<_x<_2pi
if y=.5, then
sinx=.5, x=30 deg, 150deg
To find the number of points of intersection between the lines 2y = 1 and y = sin(x), where -2π ≤ x ≤ 2π, we can solve these equations simultaneously.
First, let's set up the equations:
1. Equation 1: 2y = 1
2. Equation 2: y = sin(x)
Now, substitute Equation 2 into Equation 1:
2(sin(x)) = 1
Simplify:
sin(x) = 1/2
To determine the solutions for x, we need to find angles in the given range where sin(x) equals 1/2. The common angles that satisfy this condition are π/6 and 5π/6 (in radians).
So, we have two solutions for the equation sin(x) = 1/2: x = π/6 and x = 5π/6.
Since the given range is -2π ≤ x ≤ 2π, both solutions lie within this interval.
Therefore, there are two points of intersection between the lines 2y=1 and y=sin(x) in the given range.