Question

cos^2(x)+cos(x)sin(x)=0 solve for x

Answer 1

Try factoring

Answer 2

I factored a cos(x) out but then im stuck

Answer 3

cos(x)( ? + ? ) =0
So what should be in the places of those ?'s once you factor out cos(x)?

Answer 4

cos(x)(cosx+sinx)

Answer 5

Yes. Set both factors equal to 0.
cos(x)=0 ; cos(x)+sin(x)=0

Answer 6

Solve cos(x)=0 for x
And find the value x so that cos(x) and sin(x) are opposites (i.e cos(x)=-sin(x))

Answer 7

cosx=pie/2 ?

Answer 8

cos(x)=0 for x=pi/2
cos(x) does not equal pi/2
But one value that satisfies cos(x)=0 is x=pi/2
Are there any other values?

Answer 9

x=3pi/2

Answer 10

Ok and you can also say we have x=pi/2+2npi where n is an integer
or x=3pi/2+2n pi where n is an integer

Answer 11

We also need to find the values of x where cos(x) and sin(x) have opposite values.

Answer 12

As you can see they will be opposite in quadrant 2 and 4.

Answer 13

These points is where cos(x) and sin(x) are opposite. Now what angle are these points at from the initial ray?