Question

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

Answer 1

Answer:cot t = 1.875

$sin t=\frac{-8}{17}$ but sin²t + cos²t = 1 ⇔ cos²t = 1 - sin²t

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

but  t is a quadrant III angle => cos t = $\frac{-15}{17}$

=> cot t = $\frac{-15}{17}:\frac{-8}{17}=\frac{15}{8}=1.875$

Step-by-step explanation: