Name five x values for which the sine function equals to 0. Please help!!

- anonymous

Name five x values for which the sine function equals to 0. Please help!!

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- Mertsj

Are you familiar with the unit circle?

- anonymous

no

- Mertsj

Then find the inverse sine of 0 and and 360 to that answer repeatedly until you have 5 values.

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- anonymous

how?

- Mertsj

With your calculator

- anonymous

I don't know how though

- Mertsj

inverse sin 0 enter

- Mertsj

What in the world are you doing that you don't know anything about the unit circle and don't know how to use your calculator?

- anonymous

i put sin 0 enter and the answer was 0 how do i get 5 values?

- anonymous

trying to learn from an oonline classs

- Mertsj

|dw:1375670932781:dw|

- Mertsj

Have you ever seen that before?

- anonymous

yeah

- Mertsj

That is the unit circle. It is called the unit circle because the radius is 1 unit. The sin is like y.

- Mertsj

Do you see that the y value is 0 at 0 degrees and 180 degrees?

- anonymous

yes

- Mertsj

Your problem says to give 5 values for which the sin is 0. There are two of them right there: 0 degrees and 180 degrees. If we would go around the circle another time, we would come to 360 degrees and 180+360 which is 540 degrees. Are you with me?

- anonymous

sorta.. so it would be 0,180,540?

- Mertsj

0,180,360,540...
Just keep adding 180 degrees because every 180 degrees, the y value (which is the sin) is 0.

- Mertsj

Or, instead of rotating counterclockwise, we could go clockwise and then the angles would be -180, -360, -540, ...

- anonymous

ohh ok thank you! i have the same question exept its cosine value

- Mertsj

Same thing except the cosine is like x.

- Mertsj

So where is the cosine 0 on the unit circle?

- anonymous

um im not sure

- Mertsj

Look at the picture I drew. For what angles is the x value 0?

- Mertsj

|dw:1375671563924:dw|

- Mertsj

How many degrees is that?

- anonymous

90?

- Mertsj

Yes.

- Mertsj

And what is the next angle where the x value is 0?

- anonymous

so it would be 90 180...?

- Mertsj

|dw:1375671659091:dw|

- anonymous

270?

- Mertsj

yes. so the x value is 0 at 90, 270, 450, 630...

- anonymous

thank you soo much i just have one more

- Mertsj

Or at -90, -270, -450...

- anonymous

same but tangent function

- Mertsj

Do you know the definition of tangent?

- anonymous

umm no

- Mertsj

tangent is equal to sin over cos
Have you ever heard that?

- anonymous

i think ive heard it

- Mertsj

\[\tan x=\frac{ \sin x}{\cos x}\]

- Mertsj

The only way a fraction can be 0 is for the numerator to be 0. So the tangent is 0 whenever the sin is 0

- anonymous

ok so then wht

- Mertsj

Are you trying to answer this question: Give 5 angles who tangent is 0?

- anonymous

the question is name five x values for which the tangent function equals to 0

- Mertsj

Could you answer this question: Name five x values for which the sine function equals to 0?

- anonymous

yeah we already did that one

- Mertsj

So did you read this post which I made a few moments ago:
"The only way a fraction can be 0 is for the numerator to be 0. So the tangent is 0 whenever the sin is 0"

- anonymous

yeah i read it but i don't understand

- Mertsj

The sin of 180 degrees is 0. Therefore the tangent of 180 degrees is also 0
The sin of 0 degrees is 0. Therefore the tangent of 0 degrees is also 0
The sin of 360 degrees is 0. Therefore the tangent of 360 degrees is also 0
The sin of 540 degrees is 0. Therefore the tangent of 540 degrees is also 0.

- anonymous

so my answer would be exactly the same as the sine one?

- Mertsj

Let's make sure you understand this.

- Mertsj

What is the sin of 180 degrees?

- anonymous

0

- Mertsj

What is the cosine of 180 degrees?

- Mertsj

\[\tan 180^{o}=\frac{\sin 180^{o}}{\cos 180^{o}}=\frac{0}{-1}=0\]

- Mertsj

I guess you've gone. Good luck.

- anonymous

yeah i get it thank you soo much!!!!

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