Question

if tan theta=5/6 and the terminal side of the quadrant is in the third quadrant.find the remaining trignometric ratios of theta.​

Answer 1

Given ,

$\star$ Tan(Φ) = 5/6 = P/B

$\star$ Φ lies in third quadrant

By Pythagoras theorem ,

(H)² = (6)² + (5)²

(H)² = 36 + 25

(H)² = 61

H = √61

Since , Φ lies in third quadrant

Sin(Φ) = -5/√61

Cos(Φ) = -6/√61

Cot(Φ) = 6/5

Sec(Φ) = -√61/6

Cosec(Φ) = -√61/5