Kalkulator trigonometri

1. fungsi trigonometri dhasar

• fungsi sinus (sin)： \( \sin(\theta) = \frac{\text{sisih ngelawan}}{\text{hipotenuse}} \)
• fungsi kosinus (cos)： \( \cos(\theta) = \frac{\text{tanggane}}{\text{hipotenuse}} \)
• fungsi tangen (tan)： \( \tan(\theta) = \frac{\text{sisih ngelawan}}{\text{tanggane}} = \frac{\sin(\theta)}{\cos(\theta)} \)
• fungsi cosecant (csc)： \( \csc(\theta) = \frac{1}{\sin(\theta)} \)
• fungsi secant (sec)： \( \sec(\theta) = \frac{1}{\cos(\theta)} \)
• fungsi cotangent (cot)： \( \cot(\theta) = \frac{1}{\tan(\theta)} = \frac{\cos(\theta)}{\sin(\theta)} \)

2. sesambetan timbal balik

• sinus timbal balik： \( \csc(\theta) = \frac{1}{\sin(\theta)} \)
• kosinus timbal balik： \( \sec(\theta) = \frac{1}{\cos(\theta)} \)
• tangen timbal balik： \( \cot(\theta) = \frac{1}{\tan(\theta)} = \frac{\cos(\theta)}{\sin(\theta)} \)

3. sesambetan kothak

• Hubungan sinus lan kosinus kuadrat： \( \sin^2(\theta) + \cos^2(\theta) = 1 \)
• Hubungan tangent lan cosecant： \( 1 + \tan^2(\theta) = \sec^2(\theta) \)
• Hubungan cotangent lan cosecant： \( 1 + \cot^2(\theta) = \csc^2(\theta) \)

4. rumus jumlah lan beda

• Sum of Sines Formula： \( \sin(a \pm b) = \sin(a)\cos(b) \pm \cos(a)\sin(b) \)
• rumus bedane jumlah cosinus： \( \cos(a \pm b) = \cos(a)\cos(b) \mp \sin(a)\sin(b) \)
• rumus tangen lan beda： \( \tan(a \pm b) = \frac{\tan(a) \pm \tan(b)}{1 \mp \tan(a)\tan(b)} \)

5. Formula produk lan bedane

• Produk Sinus lan Formula Bedane： \( \sin(a)\sin(b) = \frac{1}{2}[\cos(a-b) - \cos(a+b)] \)
• Formula Produk Cosine lan Bedane： \( \cos(a)\cos(b) = \frac{1}{2}[\cos(a-b) + \cos(a+b)] \)
• produk tangen lan rumus beda： \( \tan(a)\tan(b) = \frac{\sin(a)\sin(b)}{\cos(a)\cos(b)} \)

6. formula produk sum-difference

• Formula produk sinus lan prabédan： \( \sin(a \pm b) = \sin(a)\cos(b) \pm \cos(a)\sin(b) \)
• Formula produk kosinus lan prabédan： \( \cos(a \pm b) = \cos(a)\cos(b) \mp \sin(a)\sin(b) \)
• rumus produk tangen lan beda： \( \tan(a \pm b) = \frac{\tan(a) \pm \tan(b)}{1 \mp \tan(a)\tan(b)} \)

7. Rumus sudut ganda

• rumus sudut sinus： \( \sin(2\theta) = 2\sin(\theta)\cos(\theta) \)
• rumus akeh sudut kosinus： \( \cos(2\theta) = \cos^2(\theta) - \sin^2(\theta) = 2\cos^2(\theta) - 1 = 1 - 2\sin^2(\theta) \)
• rumus sudut tangen： \( \tan(2\theta) = \frac{2\tan(\theta)}{1 - \tan^2(\theta)} \)

8. rumus setengah amba

• Rumus setengah sudut sinus： \( \sin\left(\frac{\theta}{2}\right) = \pm \sqrt{\frac{1 - \cos(\theta)}{2}} \)
• rumus setengah sudut kosinus： \( \cos\left(\frac{\theta}{2}\right) = \pm \sqrt{\frac{1 + \cos(\theta)}{2}} \)
• rumus setengah sudut tangen： \( \tan\left(\frac{\theta}{2}\right) = \frac{1 - \cos(\theta)}{\sin(\theta)} = \frac{\sin(\theta)}{1 + \cos(\theta)} \)

9. nilai sudut khusus

sudut	sin(θ)	cos(θ)	tan(θ)	csc(θ)	sec(θ)	cot(θ)
30°	\( \frac{1}{2} \)	\( \frac{\sqrt{3}}{2} \)	\( \frac{1}{\sqrt{3}} \)	\( 2 \)	\( \frac{2}{\sqrt{3}} \)	\( \sqrt{3} \)
45°	\( \frac{\sqrt{2}}{2} \)	\( \frac{\sqrt{2}}{2} \)	1	\( \sqrt{2} \)	\( \sqrt{2} \)	1
60°	\( \frac{\sqrt{3}}{2} \)	\( \frac{1}{2} \)	\( \sqrt{3} \)	\( \frac{2}{\sqrt{3}} \)	2	\( \frac{1}{\sqrt{3}} \)
90°	1	0	\( \infty \)	1	\( \infty \)	0