Question

How do you convert sin(arctan(5)) = 0.980580676 into a radian in terms of pi? Example 2pi/3.

Answer 1

That number cannot be changed into a nice form of pi

Answer 2

How would you go about it?

Answer 3

I am using an online tool to record answers to the question and it requires the answer to be in pi form.

Answer 4

as 5/sqrt(26) cannot be changed into that nice form.

Answer 5

You would just square the entire equation and end up with 25/26.

Answer 6

that number 5/sqrt(26) does not represent an angle; it represents the sine of the angle theta (where theta is the angle whose tan is 5).

Answer 7

So where do you get sqrt(26) from?

Answer 8

where did you get your answer 0.9805.... ? from a calculator?

Answer 9

yes. I don't know how to do the arctan and sin functions on paper yet.

Answer 10

Do you?

Answer 11

Please share.

Answer 12

On an exam, if you were asked for the exact value of sin(arctan(5)), you would need to write 5/sqrt(26).

Watch.........

Answer 13

In the diagram, tan theta = 5. agree?

Answer 14

yes

Answer 15

Now, when ytou are asked for sin(arc tan 5))...you are really being asked to find the sin of theta...whete theta is tan of 5.

So what is sin of theta?

sin of theta is opposite leg/hypotenuse...

Answer 16

By pythagorean theorem...1^2 + 5^2 = y^2
0r, 1 + 25 = y^2
26 = y^2
y = sqrt(26)

Answer 17

so sintheta = 5/sqrt(26)..thats the exact answer.

Answer 18

If you go to your calculator and plug in 5/sqrt(26) , you get that decimal.

Answer 19

But the EXACT value of sin(arctan 5)) is 5/sqrt(26).

Answer 20

okay thank.

Answer 21

So that number represents the value of the sin of theta.

Answer 22

Thank you very much Easyaspi314.

Answer 23

It does not represent an angle, where you can convert to radians.

And even if that were to represent an angle (which it does NOT), you cant convert it to radian measure in a nice form of pi, anyways.

Answer 24

Sorry for going on and on...but wanted to make that point crystal clear.

Answer 25

Alright, I understand where I was confused and thus confusing you. I was wondering how to get the fractional answer for the sin of theta, but was actually asking for the pi form of the angle. Thanks.

Answer 26

And, BTW, using your calculator does not always prove beneficial. If you were to be asked to find cos(tan (x/7)), then your calculator is worthless. But the way I showed you, the answer becomes very clear.

Answer 27

I meant cos(arctan (x/7))

Answer 28

Thanks I will be using that form from now on. I dislike using a calculator and definitely prefer to work the problems on paper or in my head.

Answer 29

a calculator wouldnt help you at all in that problem.

Answer 30

OK. You're welcome.