Question

Need help with the answer! When answering, please specify which answers go in the box, I shouldn’t have to guess. Please and thank you!!

Answer 1

The real zeros of the trigonometric function on the interval 0 ≤ x ≤ 2·π are;

x = π/3, 2·π/3

The details of the steps used to find the zeros are as follows;

The zeros of the trigonometric function f(x) = sin(2·x) - (√3)·cos(x) are required

The zeros are the x-values (input values) where the output value of the function, f(x), is zero as follows;

f(x) = 0

0 = sin(2·x) - (√3)·cos(x)

sin(2·x) = (√3)·cos(x)

sin(2·x) = 2·sin(x)·cos(x)

2·sin(x)·cos(x) = (√3)·cos(x)

2·sin(x)·cos(x)/cos(x) = (√3)

2·sin(x) = (√3)

sin(x) = (√3)/2

x = arcsin((√3)/2)

x = π/3, or x = 2·π/3