anonymous
  • 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
Mathematics
schrodinger
  • schrodinger
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anonymous
  • anonymous
anyone? please.
anonymous
  • anonymous
I can't access it because it directs me to the log in page of the website.
anonymous
  • anonymous
let me try it another way

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anonymous
  • anonymous
|dw:1438578342154:dw|
anonymous
  • anonymous
this is what it looks like
anonymous
  • anonymous
i am trying it and i got 0.625 for the sin.
anonymous
  • anonymous
How did you get 0.625? What did you do?
anonymous
  • anonymous
These are the 6 trigonometric functions btw. |dw:1438578372182:dw|
anonymous
  • anonymous
figured up the hypotenuse at 19.2 and then i took the opposite which is 12 and divided it by the hypotenuse.
anonymous
  • anonymous
Should your answers be in decimal or fractions?
anonymous
  • anonymous
wasn't specified
anonymous
  • anonymous
so i just did it in decimals.
anonymous
  • anonymous
I'd suggest you'll write in fractions. :)
anonymous
  • anonymous
okay so should i convert it over?
anonymous
  • anonymous
usually if its not how the computer wants it my teacher fixes it but i can always do it in fractions.
anonymous
  • 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
  • anonymous
okay.
anonymous
  • anonymous
It is always easier to convert from fractions to decimals than from decimals to fractions. XD
anonymous
  • anonymous
i noticed lol
anonymous
  • anonymous
Did you see the image above? About the six trigo functions? Just apply it.
anonymous
  • anonymous
yes
anonymous
  • 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
  • anonymous
Still there?
anonymous
  • anonymous
yeah trying to figure it out
anonymous
  • anonymous
Hmmm don't use your calculator. Just plug in the numbers then that's it. Let this be in fraction form.
anonymous
  • anonymous
im not using a calculator I'm just that bad at math
anonymous
  • anonymous
12/3sqrt41
anonymous
  • anonymous
Correct.
anonymous
  • anonymous
thats how i do it?
anonymous
  • anonymous
that easy?
anonymous
  • anonymous
Yes. :)
anonymous
  • anonymous
theres no way its that easy
anonymous
  • anonymous
But... you need to rationalize it because the denominator is in radical form.
anonymous
  • anonymous
so how do i do that?
anonymous
  • anonymous
Multiply both the numerator and denominator with the denominator.
anonymous
  • anonymous
|dw:1438579262504:dw|
anonymous
  • anonymous
Solve it, then that's the sine.
anonymous
  • anonymous
I'll help you. :D What is 12 times 3?
anonymous
  • anonymous
36
anonymous
  • anonymous
sorry, I'm bad when it comes to anything with square roots
anonymous
  • anonymous
So the numerator will be 36 sqrt 41.
anonymous
  • anonymous
|dw:1438579466792:dw|
anonymous
  • anonymous
ok.. now?
anonymous
  • anonymous
For the denominator, just remove the radical sign, then multiply.
anonymous
  • anonymous
so 9?
anonymous
  • anonymous
No. Since we removed the radical sign, it will now be 3 times 41.
anonymous
  • anonymous
ok so 123
anonymous
  • anonymous
You forgot to multiply the other 3. :)
anonymous
  • anonymous
this is so complicated lol
anonymous
  • anonymous
|dw:1438579699524:dw|
anonymous
  • anonymous
369
anonymous
  • anonymous
Yes! :D
anonymous
  • anonymous
Then simplify it. |dw:1438579781076:dw|
anonymous
  • anonymous
so is that the answer?
anonymous
  • anonymous
But we need to simplify it first.
anonymous
  • anonymous
lol its never actually done
anonymous
  • anonymous
HAHAHA one more step, then that's it; I promise. :D
anonymous
  • anonymous
ok.
anonymous
  • anonymous
Do you know how to simplify it?
anonymous
  • anonymous
no
anonymous
  • anonymous
:(
anonymous
  • anonymous
Oh so we just need to find all of the factors of the numerator and denominator.
anonymous
  • anonymous
Do you know the factor of 36? What do you multiply to get 36?
anonymous
  • anonymous
2
anonymous
  • anonymous
2 and ?
anonymous
  • anonymous
18
anonymous
  • anonymous
Great! So what are the numbers you'll multiply to get 18?
anonymous
  • anonymous
Do you know the factor tree?
anonymous
  • anonymous
i know how to simplify but not with the numerator being a square root
anonymous
  • anonymous
Just ignore the square. :D
anonymous
  • anonymous
So just simplify 36/369.
anonymous
  • anonymous
okay
anonymous
  • anonymous
So what's the answer?
anonymous
  • anonymous
4/41
anonymous
  • anonymous
sorry my laptop was at 1% and it wasn't charging so i was trying to fix that lol
anonymous
  • anonymous
Good! So you just need to put back the sq rt of 41 to the numerator, then that's the sine.
anonymous
  • anonymous
For cosine, just do what we did in the sine.
anonymous
  • anonymous
so 4sqrt41/369?
anonymous
  • anonymous
You already simplified it, why did you put back 369? :D
anonymous
  • anonymous
i meant 41 I'm losing it lol
anonymous
  • anonymous
i was looking back over everything lol
anonymous
  • anonymous
Lol yes that's the sine.
anonymous
  • anonymous
Now do the cosine.
anonymous
  • anonymous
i think i got it from here. i can look back over it all.. thank you :)
anonymous
  • anonymous
Sure! Once you did cosine, everything is now easy. Do you know how to get the tan now?
anonymous
  • anonymous
What makes it harder is the rationalizing of the radicals, right? :D
anonymous
  • anonymous
yes, thank you so much!
anonymous
  • anonymous
you're welcome! if you need any help, just tag me.
anonymous
  • anonymous
awesome! thanks!

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