list all the x intercepts for y3cos4x13pi on the interval pi

list all the x intercepts for y=-3cos(4x+1/3pi) on the interval [-pi/6,pi/2]

Solution

y = - 3 cos ( 4x + 1/3 pi )

to find x intercepts plug y = 0

- 3 cos ( 4x + 1/3 pi ) = 0

4x + 1/3 pi = n* pi

4x = npi - pi/3

x = npi/4 - pi/12

for n=0

x = -pi/12

for n = 1

x = pi/6

n = 2

x = pi/2 - pi/12 = 5pi/12

in the interval [ -pi/6 , pi/2 ]

x intercepts = -pi/12 , pi/6 , 5pi/12