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anonymous
 one year ago
Will anybody explain to me how Sine Cosine and Tangent works? I missed school when they taught us, and when they tried to explain it to me I became brutally lost. :)
anonymous
 one year ago
Will anybody explain to me how Sine Cosine and Tangent works? I missed school when they taught us, and when they tried to explain it to me I became brutally lost. :)

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zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1Our trigonometric functions allow us to relate `the angle` of a triangle to its `sides`.

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1We have this clever acronym for remembering the relationships:\[\Large\rm \color{red}{\text{Soh}}\color{green}{\text{Cah}}\color{royalblue}{\text{Toa}}\] The `sine` of an angle is equivalent to the ratio of the `opposite` side to the `hypotenuse`. That's what the `o` and `h` stand for.\[\large\rm \color{red}{\sin x=\frac{opposite}{hypotenuse}}\]

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1Let's first look at a right triangle, and make sure we understand how to label the sides.

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1dw:1444603738782:dwSo if this is my triangle, with angle x labeled here. Do you know which side to label as your `hypotenuse`?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0The side that is on top of the x, aka the "long side"

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1Good. The longest side. Another way I like to think of it, is in relation to the `right angle`. It's always the side `opposite the right angle`.dw:1444604392651:dw

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1Hmm with that idea in mind... Which side do you think we would label as being located `opposite angle x`?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0The side that is vertical. all the way to the right.

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1dw:1444604552006:dwOk great. So the last side we label as being `adjacent` or `next to` or angle x.

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1dw:1444604621344:dwSo if I have a particular triangle like this one, based on our definition of sin x, do you have an idea of how to find it using these values? :)

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1No no, you're getting too fancy. Using something like Inverse Sine would allow us to figure out our angle x, yes. But we weren't up to that point yet XD We just want \(\large\rm \sin x=?\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I thought you said to find the angle :P so we want sin(x) which sine is Soa so Opposite over Adjacent?

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1Woooops :O\[\Large\rm \color{red}{\text{Soh}}\color{green}{\text{Cah}}\color{royalblue}{\text{Toa}}\]Soh, not Soa ya silly billy >.<

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Oh my lord x_x How did i even pass math class... SO! It'd be Opposite over Hypotenuse, yes?

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1Ok good.\[\large\rm \color{red}{\sin x=\frac{opposite}{hypotenuse}}\]Based on the way we labeled these sides, it looks like we're using the 4 and 5, ya?\[\large\rm \color{red}{\sin x=\frac{4}{5}}\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Yes yes. That's what the triangle tells us.

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1And ya, if we wanted to solve for the angle, we could apply the inverse sine function,\[\large\rm \arcsin\left(\sin x\right)=\arcsin\left(\frac{4}{5}\right)\]On the left you the composition of a function and it's inverse, which gives us back the argument,\[\large\rm x=\arcsin\left(\frac{4}{5}\right)\]

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1dw:1444605278799:dwIf that's too confusing, another way to think of it is... When you change from sine to inverse sine, you just switch the stuff,

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0.O. ohh my... but one question... So i was told if you do normal sine, and you go to find the hypotenuse, your equasion would look something like this: 5/sin(x)= adjacent? Why is this?

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1dw:1444605485213:dwOk let's see if we can do something with this triangle.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0*dies* x_x okayyy umm... SOH... 4/sin(30degrees) which will give us the adjacent...

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Opposite. it gives us the opposite.

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1Yah let's ignore the adjacent for now :) If we want to solve for \(\large y\),the opposite side, Then we want to pay attention to THIS stuff,dw:1444605655180:dw

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1Mmm k good. And how would you `isolate` the y? You want to solve for y, so you need to get it alone somehow. It's being `divided` by 4 right now. How can we undo that?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0multiply it by 4. which means we have to do it to the other side so 4times sin(30) = y

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1Good. And keep in mind that this 30 is like... locked in the sine function, he can't interact with the 4 in any way.\[\large\rm 4\sin(30)\ne \sin(4\cdot30)\]

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1\[\large\rm y=4\sin(30)\]And you would just use your calculator to finish that one off, unless of course you've learned about your 30/60/90 triangle, in which case you might be able to do it without a calculator.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So then we'd do sin(30) first. then multiply the answer by 4?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I got 2 when i plugged it into my calculator.

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1Yay good job! How would solve for the adjacent side, x? Let's pretend that we don't know what y is. So we can make sure of our cosine definition.

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1dw:1444606171089:dwAgain, we don't want more variables than x. So we're dealing with these three pieces of information, ya?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Alright... so CAH... Cos(30)= x/4

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0and with that we'd need x alone so we multiply it by both sides correct?

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1\[\large\rm \cos(30)=\frac{x}{4}\]Multiply 4? Ok seems like a good idea:\[\large\rm 4\cos(30)=\frac{x}{\cancel4}\cdot\cancel4\]\[\large\rm 4\cos(30)=x\]And unfortunately, this one is going to work out to a weird decimal length, but that's ok.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I got 3.46 for x o.o

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1Here is a nice way to check your work: Recall that your hypotenuse should be the `longest side`. 3.46 is shorter than 4 \(\large\rm \color{green}{\checkmark}\) I tried to also draw that angle somewhat accurately to be a 30 degree angle. So if that vertical length is 2, would 3.5 be about right for the bottom length? yaaa that's prolly right!

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Seems easy enough to remember.

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1dw:1444606546042:dwLet's try this problem. We need to find the length of the hypotenuse, z.

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1\[\large\rm \cos(30)=\frac{5}{z}\]Ok good. Hmmm, notice our z is in the denominator, this makes things a little trickier. Any ideas? :o

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Uhhh.... divide five by both sides?...

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1Ya let's try that:\[\large\rm \frac{1}{5}\cdot\cos(30)=\frac{\cancel5}{z}\cdot\frac{1}{\cancel5}\]The z is still stuck in the denominator though! Ok you had the good sense to flip it after that though?\[\large\rm \frac{\cos(30)}{5}=\frac{1}{z}\qquad\to\qquad \frac{5}{\cos(30)}=z\]

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1Or maybe you got lucky :) I'm not sure which lol

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0XD im pretty sure i got lucky... i didn't even realize i skipped a whole piece.

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1When your variable is stuck in the denominator, these are the steps I would recommend:\[\large\rm \cos(30)=\frac{5}{z}\]Multiply both sides by z,\[\large\rm z\cos(30)=5\]Divide both sides by cos(30),\[\large\rm z=\frac{5}{\cos(30)}\]

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1So when your variable is stuck in the bottom, the process is a little bit different. Just a bit trickier.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Indeed. When I plugged the equation in, I got 3.8

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1Ok, again let's check our work. The hypotenuse should be the longest side. But our adjacent side is 5. Uh oh! 3.8 < 5

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0My second time i got 5.8 when i did Cos(30), got my answer, then divided 5 by my answer (5/ ans is what im trying to say...)

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1Do you have a calculator that uses the "Ans" thing?

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1Ya I really like that feature. You can do the problem all at once, \(\large\rm 5\div\cos(30)\) Or in parts as you described, \(\large\rm \cos(30)\quad \boxed{=}\) \(\large\rm 5\div Ans \quad \boxed{=}\) Whichever way makes more sense to you :)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0They both do. But sometimes double checking prevents me from making a mistake, gladly.

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1I need a math break I think :) lol Too much maf. Here is one more you can work on though.

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1So if you get bored and wanna try another one, try to solve for x in that triangle :)

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1I'mma go make some foods a sec >.<

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Alright. I'll attempt to figure this one out. and you enjoy your food. I need a math break after this too XD I have alot more homework... lol

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Tan(41)=7/x 7/tan(41)=x 7/tan(41)= 8.1 That's what I got.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Lol then i got 10.7 for the hypotenuse using the same opposite.

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.17/tan(41)=8.05, so ya 8.1 sounds good. 10.7? 0_o weird
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