Question

Solve the equation in the interval [0. 2pi)
cosx sinx - sinx = 0

Answer 1

sin(x) (cos(x)-1) = 0
=> sin(x) = 0 OR cos(x) = 1

Find x from that...and in the interval given.

Answer 2

The book says the answer is 0, pi but I don't understand how they got there

Answer 3

sin(x) = 0 when x = 0 and x = 180 degrees (pi radians).

Answer 4

cos(x) = 1 when x = 0 and x = 360 degrees, which is 2pi, but 2pi is NOT in the domain given. So, the right answer is 0 or pi.

Answer 5

So question????
Did you just factor out the sinx out of this problem and set it equal to zero?
And with cosx-1 left over you moved the 1 to the other side?

Answer 6

YES. YES!

Answer 7

thanks

Answer 8

When a product of two things is zero, either or both can be zero.
So, when sin(x) (cos(x)-1) = 0, either sin(x) = 0 OR cos(x)-1 = 0.
=> sin(x) = 0 OR cos(x) = 1.