Yes my first intuition was to substitute x+y = t And for solving the integral i used the 2nd method ,as it's pretty standard for integral involving cos and sin Nice video syber
@@kevinmadden1645 Tangential in common speech comes from the idea that a tangent line is scarely intersecting the circle and diverges from the circle as you follow the tangent line: "going off on a tangent". As a function we can also relate tan(theta) to the unit circle: I'm sure you are familiar with the unit circle and ray from the origin setup that gets us sin(theta) and cos(theta). Now add a tangent line to the circle at (1,0) and extend the ray to intersect this tangent line, call that point T. tan(theta) is the vertical distance of this line from (1,0) to T. This also gives us sec(theta) as the distance from the origin to T.
@@kevinmadden1645The fact that you admit that you don't understand how the tangent line relates to sine divided by cosine, which is exactly tangent, explains everything. This is tangential, because it's a tangent function, which is by definition tangent. You're attempting to claim a singular use of the word tangential isn't suitable for this equation, when going off on a tangent is exactly what the length of the tangent line (the value of the tangent function) is in relation to the unit circle and trigonometry and its role as a transcendental function in general.
Yes my first intuition was to substitute x+y = t
And for solving the integral i used the 2nd method ,as it's pretty standard for integral involving cos and sin
Nice video syber
Once again, nice explanation and good problem to remember a lot of advanced algebra 🤩
Nice explanation there
But this is on the easier side
Got the second approach on the first try.
Love your content❤❤
Awesome! Thank you!
So disappointed in Wolfram Alpha's solution to this d.e.
You mean lack of solution
Very good. Thanks 👍
Thank you too!
Good Problem and Nice Explanation!
Thank U!
You are welcome
Math is heart
❤️
Tangential is misused here. Tangential means slightly related to scarcely bordering upon. It has nothing to do with the tangent function.
It is misused in this case but the tangent function is related to tangential
@@Alians0108 How?
@@kevinmadden1645
Tangential in common speech comes from the idea that a tangent line is scarely intersecting the circle and diverges from the circle as you follow the tangent line: "going off on a tangent". As a function we can also relate tan(theta) to the unit circle:
I'm sure you are familiar with the unit circle and ray from the origin setup that gets us sin(theta) and cos(theta). Now add a tangent line to the circle at (1,0) and extend the ray to intersect this tangent line, call that point T. tan(theta) is the vertical distance of this line from (1,0) to T. This also gives us sec(theta) as the distance from the origin to T.
@@bsmith6276 Your explanation is valid for a tangent line. I do not understand the connection if you define the tangent trig function as sine/cosine.
@@kevinmadden1645The fact that you admit that you don't understand how the tangent line relates to sine divided by cosine, which is exactly tangent, explains everything. This is tangential, because it's a tangent function, which is by definition tangent. You're attempting to claim a singular use of the word tangential isn't suitable for this equation, when going off on a tangent is exactly what the length of the tangent line (the value of the tangent function) is in relation to the unit circle and trigonometry and its role as a transcendental function in general.