Question

how many solutions does the equation sin(4x) = 1/2 have on the interval (0,2pi)

Answer 1

count intersection blue and red

Answer 2

this only one way to solve the question..

Answer 3

say 4x=a

sina=1/2
what could be a?
a=pi/6 right

what else?

a=n*pi+pi/6 n in Z

4x=n*pi+pi/6

x=1/4(n*pi+pi/6)

n=0,1,2,3,4,5,6,7,8 but not 9

because n=9

1/4(9*pi+pi/6=7.19>2pi=6.28

Answer 4

sorry n=8 is also not working
1/4(8*pi+pi/6=6.41>2pi=6.28

so answer is 8

Answer 5

thank you!!

Answer 6

np