到底要怎樣解sin(x^2)=sin(x)

[@bprptw]

怎樣找出x^2=2^x所有的答案 ? kzbin.info/www/bejne/hpCtopV8fLF-o6c

[@hsiehcharrly9443]

問一下，"^"這個符號怎麼自鍵盤打出來

[@徐中-x1n]

Ctrl+^ (^跟6、ˊ應該同一格)

[@lazarusisaacng]

這種解法可以對不熟悉三角函數的示範了一個最好的解法。👍

[@chromalol08013]

this guy is a legend in both English and Chinese

[@koktonglan7566]

sin(x²)=sin(x) sin(x²)-sin(x)=0 2sin(x²-x/2)cos(x²+x/2)=0 (1-cos(x²-x))(1-cos(x²+x)=0 1-cos(x²-x)=0 1-cos(x²+x)=0 cos(x²-x)=1 x²-x=2nπ x²+x=2nπ # 剩下用quadratic formula

[@penguincute3564]

Wait black pen red pen has a Chinese channel?

[@phoenixarian8513]

Yep. sin(x) is periodic function therefore you have to consider the period! all same offsets over the period will result in the same results! sinx=sin(x+2npi) n to be any integer However this is half of the solution. The other is "mirroring" and x=pi/2 is the mirror axis. This leads to as you mentioned sinx=sin(pi-x) for example when x=36 degrees or pi/5 it's sin(pi/5)=sin(4pi/5). So it's 2 cases 2 sets of solutions!

[@emeraldng2910]

sin(x) = sin(a) General solution是不是應該可以直接寫成 x = n*pi + (-1)^n * a

[@PanGibson_tw]

sinx(sinx-1)=0 ⇒sinx=0 or 1 ⇒x=nπ or π/2+2nπ

[@ouo9389]

第一眼看到會覺得把sin拔掉討論很麻煩 用sina-sinb=2cos((a+b)/2)sin((a-b)/2)直接應該單純很多w

[@昆仑云路]

這個題最終要解一元二次方程。有無數個解。

[@skbmoon0017]

做積分用trig sub的時候為什麼可以用u=sin x or u=tan x?明明這兩個也不是one to one？🧐

[@劉永昌-g7g]

Trig substitution 重點是求值，x的值可以有很多個，但計算出來對應的值是一樣的

[@bprptw]

你的問題很好, 不定積分的話幾乎沒關係, 定積分的變數變換真的要小心 這部影片的第一個例子給你參考一下: kzbin.info/www/bejne/gIeZp6SuqpKaack

[@stupiddog7841]

愛了

[@chemistryka]

你他娘還真是個天才😂