- anonymous

Find the values of the six trigonometric functions for angle Θ.
https://my.dcdal.org/pluginfile.php/3759/question/questiontext/10967/1/5436/1.jpg

- schrodinger

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- anonymous

anyone? please.

- anonymous

I can't access it because it directs me to the log in page of the website.

- anonymous

let me try it another way

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## More answers

- anonymous

|dw:1438578342154:dw|

- anonymous

this is what it looks like

- anonymous

i am trying it and i got 0.625 for the sin.

- anonymous

How did you get 0.625? What did you do?

- anonymous

These are the 6 trigonometric functions btw. |dw:1438578372182:dw|

- anonymous

figured up the hypotenuse at 19.2 and then i took the opposite which is 12 and divided it by the hypotenuse.

- anonymous

Should your answers be in decimal or fractions?

- anonymous

wasn't specified

- anonymous

so i just did it in decimals.

- anonymous

I'd suggest you'll write in fractions. :)

- anonymous

okay so should i convert it over?

- anonymous

usually if its not how the computer wants it my teacher fixes it but i can always do it in fractions.

- anonymous

You're right that the hypotenuse is 19.2, but let's convert it with radicals :) So the hypotenuse is |dw:1438578691977:dw|

- anonymous

okay.

- anonymous

It is always easier to convert from fractions to decimals than from decimals to fractions. XD

- anonymous

i noticed lol

- anonymous

Did you see the image above? About the six trigo functions? Just apply it.

- anonymous

yes

- anonymous

Let's start with sine. \[\huge sine=\frac{ opposite }{ hypotenuse }\]
We know that the opposite=12, adjacent=15, and hypotenuse=3 sqrt 41. So what would sine be?

- anonymous

Still there?

- anonymous

yeah trying to figure it out

- anonymous

Hmmm don't use your calculator. Just plug in the numbers then that's it. Let this be in fraction form.

- anonymous

im not using a calculator I'm just that bad at math

- anonymous

12/3sqrt41

- anonymous

Correct.

- anonymous

thats how i do it?

- anonymous

that easy?

- anonymous

Yes. :)

- anonymous

theres no way its that easy

- anonymous

But... you need to rationalize it because the denominator is in radical form.

- anonymous

so how do i do that?

- anonymous

Multiply both the numerator and denominator with the denominator.

- anonymous

|dw:1438579262504:dw|

- anonymous

Solve it, then that's the sine.

- anonymous

I'll help you. :D What is 12 times 3?

- anonymous

36

- anonymous

sorry, I'm bad when it comes to anything with square roots

- anonymous

So the numerator will be 36 sqrt 41.

- anonymous

|dw:1438579466792:dw|

- anonymous

ok.. now?

- anonymous

For the denominator, just remove the radical sign, then multiply.

- anonymous

so 9?

- anonymous

No. Since we removed the radical sign, it will now be 3 times 41.

- anonymous

ok so 123

- anonymous

You forgot to multiply the other 3. :)

- anonymous

this is so complicated lol

- anonymous

|dw:1438579699524:dw|

- anonymous

369

- anonymous

Yes! :D

- anonymous

Then simplify it. |dw:1438579781076:dw|

- anonymous

so is that the answer?

- anonymous

But we need to simplify it first.

- anonymous

lol its never actually done

- anonymous

HAHAHA one more step, then that's it; I promise. :D

- anonymous

ok.

- anonymous

Do you know how to simplify it?

- anonymous

no

- anonymous

:(

- anonymous

Oh so we just need to find all of the factors of the numerator and denominator.

- anonymous

Do you know the factor of 36? What do you multiply to get 36?

- anonymous

2

- anonymous

2 and ?

- anonymous

18

- anonymous

Great! So what are the numbers you'll multiply to get 18?

- anonymous

Do you know the factor tree?

- anonymous

i know how to simplify but not with the numerator being a square root

- anonymous

Just ignore the square. :D

- anonymous

So just simplify 36/369.

- anonymous

okay

- anonymous

So what's the answer?

- anonymous

4/41

- anonymous

sorry my laptop was at 1% and it wasn't charging so i was trying to fix that lol

- anonymous

Good! So you just need to put back the sq rt of 41 to the numerator, then that's the sine.

- anonymous

For cosine, just do what we did in the sine.

- anonymous

so 4sqrt41/369?

- anonymous

You already simplified it, why did you put back 369? :D

- anonymous

i meant 41 I'm losing it lol

- anonymous

i was looking back over everything lol

- anonymous

Lol yes that's the sine.

- anonymous

Now do the cosine.

- anonymous

i think i got it from here. i can look back over it all.. thank you :)

- anonymous

Sure! Once you did cosine, everything is now easy. Do you know how to get the tan now?

- anonymous

What makes it harder is the rationalizing of the radicals, right? :D

- anonymous

yes, thank you so much!

- anonymous

you're welcome! if you need any help, just tag me.

- anonymous

awesome! thanks!

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