Sides can absolutely be different. However, the ratios of the sides are the same IF the angles are the same. So since we know the tangent of 45 is 1, then the ratio of the opposite to the adjacent is ALWAYS 1 if the angle is 45 degrees. Let me know if that makes sense.
Thank you a lot. I still haven't got the answer to the question How do I use them? In other words, knowing the proportions, how do I use that information. There must be a context why the ratio information deserved its own reserved names in form of trigonometric functions. Thanks!
as a child I was asked a logic question which was "Why are manhole covers round?" The beginning of your video would be a huge clue, I wish I had back then
It's been said that the hypothesis in the right triangle has the longest length, that may be true in a rectangle but, does that hold true for a 45° 45° 90° angle? I will add that a rectangle has two scaling triangles and a square has two isosceles triangles 1+1 = 2; whereas the hypotenuse in one is longer and the hypotenuse in the other are equal.
So there is a theorem that states that the longest side of a triangle is always opposite the longest side and the shortest side is opposite the smallest angle. True for all triangles, regardless of angle measures. Second theorem states that all triangles will have a sum of the three angles = 180 degrees. Now, a right triangle has to have a 90 degree angle. That means the other two angles are both less than 90 (for all to sum to 180). That by default make the 90 degree angle the largest, so the hypotenuse is the largest size. Does that make sense?
well i came here out of curiosity about angles and sin...... wow - you just hooked me talking about how it can be used in carpentry and home improvement
Unless it's one of the special ratios (for 30, 45)you have to have a table to interpolate the results to come up with an angle. You can create your own table by building a bunch of triangles and writing down the measurements. It would be the same as the trig tables from a book because a particular angle will always create the same ratios regardless of the size of your triangle. I hope that makes sense.
@@anteconfig5391 not in degrees because that is simply a comparison to know ratios. In radians it's possible. So if you know two sides, you can compute the third. Now if you inscribed that triangle inside of a unit circle (radius of 1) with one side one the x-axis and the hypotenuse touching the outside of the circle. Now measure the arc length of the circle from the x-axis to the point where the hypotenuse touches. That measurement IS the inscribed angle in radians. If you have a 3 4 5 triangle for example, the hypotenuse has to be length of 1 (to fit in unit circle), so you would divide all measurement by 5 to inscribe into the unit circle.
* THIS IS EXACTLY WHAT I NEEDED BACK IN ELEMENTARY SCHOOL!! * Fuck. all those years gone down the fucking drain because someone decided that i didn't need to understand... They told me to memorize the procedure and it'll all be fine. * IT WASN'T FINE *
OMG, this is beautifully explained, you should be teaching professors, these smart stupid people think everyone knows what they're talking about, we want to, I promise, I almost like I got ya factor that pleases them
Yes but what is the logic behind these rules? You didn't tell me the real definition about cosine and sine, isn't that th most important part te understand maths? In this case you were going to explain what they are.
These aren't rules, but they are definitions. Sine of an angle is defined as opposite/hypotenuse. It is a ratio. So in Geometry, if you have a particular angle, the opposite and the hypotenuse will always make the same ratio (regardless of how large the triangle is). I explain this at the 7 minute mark. Hope this helps.
I understand your question. The problem of current education, is they go straight to define functions but dont explain, what is that function is all about and were it came from. This is a long discussion. Anyhow my understanding of cosine/ sine functions are functions that are realated to something that happens and repeat it self periodicaly. Each angel gives you a location of ( something moving) at a particular time. In fact Sine function is the same function like Cosine but shifted by 90 deg. Tangent function is a line that touches that moving point at particular angel. I hope this give you a start to think about these functions differently than what is tought you in the school, just to pass the exam without knowing the essence of these functions.
Best way to remember trig definitions I have seen yet.. very nice 👍
I don't know why, but my teacher was being cryptic with this, saying SOH CAH TOA whenever I asked what they do/meant, thanks for clearing this up :D
Fantastic teacher. Thanks.
Thanks. Absolutely useful. Do this two figures consistently have this exact numbers for sides? I mean sides can be different or not?
Sides can absolutely be different. However, the ratios of the sides are the same IF the angles are the same. So since we know the tangent of 45 is 1, then the ratio of the opposite to the adjacent is ALWAYS 1 if the angle is 45 degrees. Let me know if that makes sense.
Yes. I realised. Thank you so much
Thank you oh so much It was never clear for me up until after this video!!
Thank you a lot. I still haven't got the answer to the question How do I use them? In other words, knowing the proportions, how do I use that information. There must be a context why the ratio information deserved its own reserved names in form of trigonometric functions. Thanks!
as a child I was asked a logic question which was "Why are manhole covers round?" The beginning of your video would be a huge clue, I wish I had back then
You might want to edit 2:45 to 2:50
Caught that too
Is that a TWSBI 540 you're using?
The original. Still a great pen. They have actually since "upgraded" it slightly.
Wish I had teaches like you - great explanations - explain hazards
Well explained, thanks. I did wonder at the need to rationalise though. 1 over root 3 seems just as easy as root 3 over 3.
Because most math books/teachers require students to rationalize. Only reason why.
@@aggieneer02 Thank you :)
It's been said that the hypothesis in the right triangle has the longest length, that may be true in a rectangle but, does that hold true for a 45° 45° 90° angle? I will add that a rectangle has two scaling triangles and a square has two isosceles triangles 1+1 = 2; whereas the hypotenuse in one is longer and the hypotenuse in the other are equal.
So there is a theorem that states that the longest side of a triangle is always opposite the longest side and the shortest side is opposite the smallest angle. True for all triangles, regardless of angle measures.
Second theorem states that all triangles will have a sum of the three angles = 180 degrees.
Now, a right triangle has to have a 90 degree angle. That means the other two angles are both less than 90 (for all to sum to 180). That by default make the 90 degree angle the largest, so the hypotenuse is the largest size. Does that make sense?
well i came here out of curiosity about angles and sin...... wow - you just hooked me talking about how it can be used in carpentry and home improvement
how can i ask you a question
Best teacher ever
Yes u are right
If all you know are the side lengths and you don't want to use a table or calculator...
How do you find the angles?
Unless it's one of the special ratios (for 30, 45)you have to have a table to interpolate the results to come up with an angle. You can create your own table by building a bunch of triangles and writing down the measurements. It would be the same as the trig tables from a book because a particular angle will always create the same ratios regardless of the size of your triangle. I hope that makes sense.
@@murphyfirearmstraining3630 So, you're saying there's no way for me to calculate the inverse sine by hand.
@@anteconfig5391 not in degrees because that is simply a comparison to know ratios. In radians it's possible. So if you know two sides, you can compute the third. Now if you inscribed that triangle inside of a unit circle (radius of 1) with one side one the x-axis and the hypotenuse touching the outside of the circle. Now measure the arc length of the circle from the x-axis to the point where the hypotenuse touches. That measurement IS the inscribed angle in radians.
If you have a 3 4 5 triangle for example, the hypotenuse has to be length of 1 (to fit in unit circle), so you would divide all measurement by 5 to inscribe into the unit circle.
Thank you, this helped so much!
Great teacher
You’re great, thank u very much, and please do some more in geometry lessons.
Is it a 🪧? 😊😊😊😊😊
Thanks, you make it easier.
* THIS IS EXACTLY WHAT I NEEDED BACK IN ELEMENTARY SCHOOL!! *
Fuck. all those years gone down the fucking drain because someone decided that i didn't need to understand...
They told me to memorize the procedure and it'll all be fine.
* IT WASN'T FINE *
OMG, this is beautifully explained, you should be teaching professors, these smart stupid people think everyone knows what they're talking about, we want to, I promise, I almost like I got ya factor that pleases them
Great vid. Thanks a lot
Thank you
Amazing
Adjecent nd opposite well these two word in Pakistan are called basic instead of adjecent nd radiculius istead of opposite..
Yes but what is the logic behind these rules? You didn't tell me the real definition about cosine and sine, isn't that th most important part te understand maths? In this case you were going to explain what they are.
These aren't rules, but they are definitions. Sine of an angle is defined as opposite/hypotenuse. It is a ratio. So in Geometry, if you have a particular angle, the opposite and the hypotenuse will always make the same ratio (regardless of how large the triangle is). I explain this at the 7 minute mark. Hope this helps.
Very good 😊 Ohhh how I wish I had these type of lessons in school 😞😞😞😞😞
I understand your question. The problem of current education, is they go straight to define functions but dont explain, what is that function is all about and were it came from. This is a long discussion. Anyhow my understanding of cosine/ sine functions are functions that are realated to something that happens and repeat it self periodicaly. Each angel gives you a location of ( something moving) at a particular time. In fact Sine function is the same function like Cosine but shifted by 90 deg. Tangent function is a line that touches that moving point at particular angel. I hope this give you a start to think about these functions differently than what is tought you in the school, just to pass the exam without knowing the essence of these functions.
yes it helped me toooo
Use this trick
SOME PEOPLE HAVE (S=P/H MEANS SINE = PERPENDICULAR ÷HYPOTENUSE)
CURLY BROWN HAIR
nice
v
I barely understand what you wrote
Ho
In my language (Urdu)I use
AO CAO AK
in English there is different
lol
wow. nobody wants to know this....