Question 419227: cosxsinx-sinx=0
I know I need to factor out sin, but I'm not sure how to do that. Found 2 solutions by duckness73, Edwin McCravy:Answer by duckness73(47) (Show Source):
You can put this solution on YOUR website! Let's rewrite the equation to make it a bit more clear:
cosxsinx - sinx = 0
(cosx)(sinx) - (sinx) = 0
This looks like an equation: ab - b = 0
If you had to factor b out of this, it would look like:
b (a - 1) = 0
So it is with the trig equation factoring out sinx
(sinx) (cosx - 1) = 0
cos(x)sin(x) - sin(x) = 0
You're not sure how to factor out sin(x)? OK, let's look at this
bit of algebra:
AB - B = 0
AB - 1B = 0
B(A - 1) = 0
Do you understand that? I put a green 1 beside the red B. Then I factored
out the red B putting the green A and the green 1 inside the parentheses.
OK, I will use the exact same color scheme, and do the exact same thing:
cos(x)sin(x) - sin(x) = 0
cos(x)sin(x) - 1sin(x) = 0
sin(x)(cos(x) - 1) = 0
Do you understand that? I put a green 1 beside the red sin(x). Then I factored
out the red sin(x) putting the green cos(x) and the green 1 inside the parentheses.
Can you go from there? If not post again. If and when you post again,
be sure to tell us whether the answer should be given in degrees or
radians (in terms of p), and whether you want
all possible solutions or just the solutions between 0 and 2p or 0 and 360°.
Edwin
