first 3 x intercepts to the right of the origin
f(x)=2cos[3(x-120)]
To find the x-intercepts of the function f(x)=2cos[3(x-120)], we need to set f(x) equal to zero and solve for x.
Setting f(x) equal to zero:
2cos[3(x-120)] = 0
Next, we can use the fact that cosine is equal to zero at certain angle values. In this case, the function will have an x-intercept when the argument of the cosine function is equal to odd multiples of pi/2.
3(x-120) = (2n+1)pi/2
Simplifying the equation:
x - 120 = (2n+1)pi/6
Solving for x:
x = (2n+1)pi/6 + 120
Since we are looking for the first three x-intercepts to the right of the origin, we need to find the values of x where n = 0, 1, and 2.
x = (2(0)+1)pi/6 + 120 = pi/6 + 120
x = (2(1)+1)pi/6 + 120 = 5pi/6 + 120
x = (2(2)+1)pi/6 + 120 = 4pi/3 + 120
Therefore, the first three x-intercepts to the right of the origin for the function f(x)=2cos[3(x-120)] are:
x = pi/6 + 120
x = 5pi/6 + 120
x = 4pi/3 + 120