Use substitution to determine whether the given x-value is a solution of the equation:
sinx = -3sqrt/2, x=4pi/3
A) Yes
B) No
C) More information is needed
D) The problem is indeterminate
A) yes
(do you not have a calculator)
To determine whether the given x-value is a solution of the equation, we can use substitution.
The equation is sin(x) = -3√2/2. We need to substitute x = 4π/3 into the equation and check if it holds true.
Step 1: Replace x with 4π/3 in the equation.
sin(4π/3) = -3√2/2
Step 2: Calculate the value of sin(4π/3).
In the unit circle, 4π/3 corresponds to an angle in the third quadrant. The reference angle is π/3, and in the third quadrant, sin values are negative. The value of sin(4π/3) is -√3/2.
Step 3: Compare the calculated value with the given value.
The calculated value, -√3/2, is not equal to -3√2/2.
Therefore, the given x-value of 4π/3 is not a solution of the equation sin(x) = -3√2/2.
The correct answer is B) No.