refer to the graph of y=sin(x) or cos(x) to find the exact values of (x) in the interval [0,4pi]that satisfy the equation.
4sin(x)=4
sin x = 1 ???
x = pi/2
x = pi/2 + 2 pi
x = pi/2 + 4 pi No - delete, out of range
y=2 cos x interval of -π, 4π
graph of y= 2 cos x on the interval -π, 4π
To find the exact values of x that satisfy the equation 4sin(x) = 4 in the interval [0, 4π], we can refer to the graph of the sine function.
Step 1: Rewrite the equation:
4sin(x) = 4
Step 2: Divide both sides of the equation by 4:
sin(x) = 1
Step 3: We know that the sine function takes on a value of 1 only at π/2 and 5π/2, within the interval [0, 4π].
The solutions for x in the interval [0, 4π] that satisfy the equation 4sin(x) = 4 are:
x = π/2, 5π/2
Note: The sine function has a period of 2π, which means that it repeats every 2π units. In the interval [0, 4π], it completes two full cycles. Therefore, the solutions are π/2 and 5π/2.