Jika sin(a) = 12 : 13, maka cot(a) = 5/12.
 

Penjelasan dengan langkah-langkah:

• sin(a) = 12 : 13
• cot(a) = ...?

Cara 1
Ingat tripel Pythagoras (5, 12, 13).
sin(a) = 12/13, maka cos(a) = 5/13.
Sehingga:
cot(a) = cos(a) / sin(a)
⇒ cot(a) = (5/13) / (12/13)
⇒ cot(a) = 5/12

Cara 2
cot(a) = cos(a) / sin(a)
⇒ cot(a) = [ √(1 – sin²) ] / sin(a)
⇒ cot(a) = [ √(1 – (12/13)²) ] / (12/13)
⇒ cot(a) = [ √((13² – 12²)/13²) / (12/13)
⇒ cot(a) = (1/13) · √(169 – 144) · (13/12)
⇒ cot(a) = (1/12) · √25
⇒ cot(a) = 5/12

Cara 3
cot²(a) + 1 = csc²(a)
⇒ cot²(a) = csc²(a) – 1
⇒ cot²(a) = 1/(sin²(a)) – 1
⇒ cot²(a) = (1/sin(a))² – 1
⇒ cot²(a) = (13/12)² – 1
⇒ cot²(a) = (13² – 12²) / 12²
⇒ cot²(a) = 5² / 12²
⇒ cot(a) = √(5² / 12²)
⇒ cot(a) = 5/12