Question

Find all solutions to the equation.

(sin x)(cos x) = 0

Answer 1

anyone help me?!?!:(

Answer 2

Hint: if

(sin x)(cos x) = 0

then

sin(x) = 0 or cos(x) = 0

Answer 3

now use the unit circle to figure out when sin(x) = 0 or when cos(x) = 0

Answer 4

@jim_thompson5910 so {(pi/2)+npi|n=0,1,2.....}?

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Answer 5

well if n = 0, then pi/2+npi turns into pi/2

but x = 0 is a solution to sin(x) = 0

Answer 6

so it's close, but not quite there

Answer 7

does that make sense?

Answer 8

@jim_thompson5910 yeaaa so what would be the correct answer?

Answer 9

a better answer would be {n*pi/2 | n = 0, 1, 2, ...}

because notice now that when n = 0, x is x = 0

when n = 1, x = pi/2

when n = 2, x = pi

etc etc

Answer 10

pretty much, any nonnegative multiple of pi/2 is a solution

Answer 11

@jim_thompson5910 {(pi/2)+npi,npi|n=0,1,2 would this be right then? {(pi/2)+npi|n=0,1,2} or this?

Answer 12

oh i see what they did, they broke it up

Answer 13

so yes it would be {(pi/2)+npi,npi|n=0,1,2, ... }

Answer 14

one is the solution set to cos(x) = 0, the other is the solution set to sin(x) = 0