Answer:
- 12 /13
Step-by-step explanation:
Given that:
Cot(θ) = 5 /12 ;
Recall ; cot θ = 1 / tan θ ; tan θ = sin θ / cos θ
Hence ;
tan θ = 1 / cot θ
tan θ = 1 ÷ (5 / 12)
tan θ = 1 * 12 /5 = 12/5
Tan θ = opposite / Adjacent = 12 /5
Sin θ = opposite / hypotenus
Hypotenus = √(opposite² + adjacent²)
Hypotenus = √12² + 5²
Hypotenus = √(144 + 25)
Hypotenus = √169
Hypotenus = 13
Hence,
Sin θ = opposite / hypotenus = 12 / 13
pi < theta < 3pi/2 lies in the 3rd quadrant ; SinΘ will be negative ;
Sin θ = - 12 /13
