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x=0 deg.

90, 360

90

Nicely explained, pace of writing is perfect. Thanks!

sin(x) + cos(x) = 1 (sin(x) + cos(x))^2 = 1^2 = 1 sin^2(x) + 2*sin(x)*cos(x) + cos^2(x) = 1 1 + 2*sin(x)*cos(x) = 1 2*sin(x)*cos(x) = 0 sin(2*x) = 0 2*x = k*pi, integer k x = (k/2)*pi, integer k

wrong calculation, that's not how a circle is calculated

If you do the same with a square, it comes out as 4

그대들수학오류 파이값의 집착 0.125 풀면 3.14+3.18 의 통합갑이라오

Why is this video 3.14 minutes?

Pi is not 3.14, of course...

Very helpful. Thank you.

X=0

You can easily deduce that this can only happen at the right angles (0, pi/2, pi, 3pi/2) through case analysis of the quadrants. In the first quadrant (0, pi/2) the sum is always greater than 1 because the sum of two side lengths of a triangle is always greater than the length of the other side. In the second and fourth quadrants (pi/2, pi) and (3pi/2, 2pi) the sum is always less than 1 because one (either cos(x) or sin(x)) is negative and the other is positive but less than 1. Finally, in the third quadrant the sum is negative. Knowing this, we just need to try these 4 angles. After testing, we can conclude that x = 0, pi/2 and all equivalent angles modulo 2pi.

+/- kpi/2

0:19 360 is not the same as 360 DEGREES. If you only write 360, you don't say anything that it is degrees you mean. You think it is 360 radians, 64800 degrees.

sin(x) + cos(x) = 1 so 1 + sin(2x) = 1 sin(2x) = 0 2x = 0, 2x = 180, 2x = 360, 2x = 540, 2x = 720 x = 0, 90, 180, 270 or 360 180 is invalid and so is 270 so x = 0, x = 180, or x = 360 On 0 <= x <= 360

I approached the question like this, 1-cosx = 2sin²x/2 & sinx = 2sinx/2cosx/2, divide both sides by sinx/2 and the equation becomes 2sinx/2 = 2cosx/2, so tan x/2 = nπ+pie/4 & sinx = 0 which is nπ.

2nπ+π/4 & 2nπ.

Good video What is the name of app you are using to design your thumbnail and font name

By Squaring both sides 1+sin2x=1 Sin2x=0 Sin2x=sin0 2x=0 X=0 degree

Never knew this ..thanks...makes so much sense now.

finally i understand pie. thank you for this amazing video. keep going 😍😍

Thanks for the video, it's actually very helpful!

sin ( x) + cos ( x) = 1 √ 2 * cos ( x - π /4) =.1 cos ( x - π /4) = 1/√2 = cos (π /4) x - π /4 = 2 n π + π /4, 2 n π - π /4 x = 2 n π + π/2, 2 n π, for imtegral n x = π /2, 0, 2π, 0 are only solution in (0, π)

Para qué elevar al ⬛.

X= 0, X= π/2. Tiene infinitas soluciones.

sin x + cos x = 1 Sqrt 2*sin (x+Pi/4)=1 Sin(x+Pi/4)=1/sqrt 2 x+Pi/4=Pi/4+2nPi x=0 or 2Pi

Good explanation at end of the video.

sinx+tg45*cosx = 1 , multiply both sides by cos45 .... you get sin(x + 45) = cos45 .....

2 sin(x) cos(x) is just sin(2x) !!! Much easier to solve this way!

such a nice detail in duration.

sinx + cosx = 1 (sinx + cosx)^2 = 1^2 = 1 2(sinx)(cosx) = 0 sinx = 0, cosx = 1 or cosx = 0, sinx = 1 x = 2nπ, (4n + 1)π/2

HOW PROGRAM USED ??

cos(x)=(e^ix+e^-ix)/2 sin(x)=-i(e^ix-e^-ix)/2 (1-i)e^ix+(1+i)e^-ix=2 1-i=sqrt(2)e^-ipi/4 1+i=sqrt(2)e^ipi/4 e^i(x-pi/4)+e^-i(x-pi/4)=sqrt(2) cos(x-45°)=1/sqrt(2) x-45°={-45°, 45°, 315°} x={0°, 90°, 360°}

Don’t need to watch. Just square both sides!!!

Another solution is to multiply both sides to √2/2 √2/2(sinx + cosx) = √2/2 √2/2sinx + √2/2cosx = √2/2 ✍️ as we know, cos45°=sin45°=√2/2 cos45°sinx + sin45°cosx = √2/2 ✍️ and it looks very similar to: sin(α+β)= sinα*cosβ + sinβ*cosα so we rewrite it as sin(45°+x)=√2/2 ✍️ and as we know, if sinx = a, (a ∈ (0;1) ) the solution is: x = (-1)^k*arcsin(a)+πk, k ∈ Z 45°+x = (-1)^k*45+180°*k, k ∈Z x = (-1)^k*45+180°k - 45°, k ∈Z we are given that x ∈[0;360°] k=0, x =45°-45°= 0✅ k = 1, x = -45+180-45=90°✅ k = 2, x = 45+360-45 = 360°✅ k = -1, x = -45-180-45 = -270 ❌ and no need to check anymore, because none will satisfy the given x I guess this is kinda a bit longer, but just wanted to write ^^ hope, I haven't done any mistakes 😅

Please make a vedio how to make animated graph