Selesaikan sin(θ_{1})=

$$\sin ( \theta _ { 1 } ) =$$

Bezakan w.r.t. θ_1

$$\cos(\theta _{1})$$

Langkah Menggunakan Takrif Terbitan

Bagi fungsi f\left(x\right), terbitannya adalah had bagi \frac{f\left(x+h\right)-f\left(x\right)}{h} apabila h pergi ke 0, jika had tersebut wujud.

$$\frac{\mathrm{d}}{\mathrm{d}\theta _{1}}(\sin(\theta _{1}))=\left(\lim_{h\to 0}\frac{\sin(\theta _{1}+h)-\sin(\theta _{1})}{h}\right)$$

Gunakan Formula Hasil Tambah untuk Sinus.

$$\lim_{h\to 0}\frac{\sin(h+\theta _{1})-\sin(\theta _{1})}{h}$$

Faktorkan \sin(\theta _{1}).

$$\lim_{h\to 0}\frac{\sin(\theta _{1})\left(\cos(h)-1\right)+\cos(\theta _{1})\sin(h)}{h}$$

Tulis semula had.

$$\left(\lim_{h\to 0}\sin(\theta _{1})\right)\left(\lim_{h\to 0}\frac{\cos(h)-1}{h}\right)+\left(\lim_{h\to 0}\cos(\theta _{1})\right)\left(\lim_{h\to 0}\frac{\sin(h)}{h}\right)$$

Gunakan fakta bahawa \theta _{1} ialah pemalar apabila mengira had semasa h pergi ke 0.

$$\sin(\theta _{1})\left(\lim_{h\to 0}\frac{\cos(h)-1}{h}\right)+\cos(\theta _{1})\left(\lim_{h\to 0}\frac{\sin(h)}{h}\right)$$

Had \lim_{\theta _{1}\to 0}\frac{\sin(\theta _{1})}{\theta _{1}} ialah 1.

$$\sin(\theta _{1})\left(\lim_{h\to 0}\frac{\cos(h)-1}{h}\right)+\cos(\theta _{1})$$

Untuk menilaikan had \lim_{h\to 0}\frac{\cos(h)-1}{h}, mula-mula darabkan pengangka dan penyebut dengan \cos(h)+1.

$$\left(\lim_{h\to 0}\frac{\cos(h)-1}{h}\right)=\left(\lim_{h\to 0}\frac{\left(\cos(h)-1\right)\left(\cos(h)+1\right)}{h\left(\cos(h)+1\right)}\right)$$

Darabkan \cos(h)+1 kali \cos(h)-1.

$$\lim_{h\to 0}\frac{\left(\cos(h)\right)^{2}-1}{h\left(\cos(h)+1\right)}$$

Gunakan Identiti Phythagoras.

$$\lim_{h\to 0}-\frac{\left(\sin(h)\right)^{2}}{h\left(\cos(h)+1\right)}$$

Tulis semula had.

$$\left(\lim_{h\to 0}-\frac{\sin(h)}{h}\right)\left(\lim_{h\to 0}\frac{\sin(h)}{\cos(h)+1}\right)$$

Had \lim_{\theta _{1}\to 0}\frac{\sin(\theta _{1})}{\theta _{1}} ialah 1.

$$-\left(\lim_{h\to 0}\frac{\sin(h)}{\cos(h)+1}\right)$$

Gunakan fakta bahawa \frac{\sin(h)}{\cos(h)+1} adalah selanjar pada 0.

$$\left(\lim_{h\to 0}\frac{\sin(h)}{\cos(h)+1}\right)=0$$

Gantikan nilai 0 ke dalam ungkapan \sin(\theta _{1})\left(\lim_{h\to 0}\frac{\cos(h)-1}{h}\right)+\cos(\theta _{1}).

$$\cos(\theta _{1})$$

Nilaikan

$$\sin(\theta _{1})$$