Question

If sin t = -8/17 and t is a quadrant III angle, find cot t

Answer 1

Answer:cot t = 1.875

`sin t=(-8)/(17)` but sin²t + cos²t = 1 ⇔ cos²t = 1 - sin²t

⇔cos t =
`\sqrt{1-sin^(2)t }=\sqrt{1-((-8)/(17))^(2) }=|(15)/(17)|`

but t is a quadrant III angle => cos t =
`(-15)/(17)`

=> cot t =
`(-15)/(17):(-8)/(17)=(15)/(8)=1.875`

Explanation: