Question

tan θ sin θ + sin θ = 0

Solve the given equation.

Answer 1

First step is to factor the left side.

Answer 2

Can you do that?

Answer 3

I'm not really sure how. This is the first type of this particular problem on my homework assignment.

Answer 4

How would you factor ax+x?

Answer 5

Factor out the X

Answer 6

Sin Theta(Tan Theta + 1) ?

Answer 7

right

Answer 8

Do you know what's next?

Answer 9

Try to get it as a single trig identity?
I'm not sure...

Answer 10

you have a product of two things: sin(theta) and tan(theta + 1) and that product equals 0, so at least one factor is 0.

Answer 11

So sin(theta)=0 or tan(theta)+1=0

Similar to how you would solve (x+1)(x+2)=0 -> x+1=0 or x+2=0 for example.

Answer 12

So I just find where they equal 0?

Answer 13

Sin theta = 0 at 2pi and pi, and tan theta = -1 at 7pi/4 ad 5pi/4

Answer 14

And then I just add on 2pi K and pi K for where Sin theta = 0 and where Tan theta = -1?

Answer 15

I think..

Answer 16

you're right about the sine part, but tan(5pi/4)=1

Answer 17

oooo 3pi/4, got the circle mixed up

Answer 18

So would the solution be 2pi+2pi k, pi + 2pi K, 7pi/4 + pi k, and 3pi/4 +pi k?

Answer 19

yes, you can simplify that though.

Answer 20

Alright
I got the question right

Answer 21

Thanks a lot!

Answer 22

I feel compelled to write down the simplified answer:
x=k pi or x= k pi -1/4 pi

Answer 23

Gotcha, My professor allows us to leave our answers unsimplified. Thanks again.

Answer 24

ok then, you're welcome.