Video narration
Poore sin x aur cos x ke graph ka inverse kyon nahin banaya ja sakta? Graph par horizontal line khinchiye: repeating sine aur cosine mein ek hi output kai inputs se milta hai. Isliye ve many-one hain. Har function ka inverse nahin hota. Iske liye function one-one hona chahiye - alag inputs ke alag outputs - aur chune hue codomain par onto, yani codomain ka har output milna chahiye. Yahin mod hai: poori repeating graph ko invert nahin karte; pehle use aisi branch par restrict karte hain jo one-one aur onto ho. Sine ke liye x ka interval [-pi/2, pi/2] lete hain, jiska range [-1, 1] hai. Isliye sin^-1 x ka domain [-1, 1], aur range [-pi/2, pi/2] hai. Cosine ki branch [0, pi] hai, range [-1, 1]. Isliye cos^-1 x ka domain [-1, 1], aur range [0, pi] hai. Sabhi endpoints shamil hain. To uttar hai: full sine aur cosine many-one hain. Sahi branch restrict karne par hi inverse well-defined banta hai.