If cot(θ)=3/5 and θ is in quadrant III, find sinθ and secθ.

Answer 1

cotT = 3/5= a/o = adjacent side over opposite side= -3/-5,

hypotenuse squared = sum of squares of adjacent side & opposite sides

h^2 = a^2 +o^2 = 3^2 +5^2 = 9+25 = 34

h = sqr34

T is in quad III where legs of the triangle are negative

a=-3, o=-5

sinT = o/h = -5/sqr34 = -5(sqr34)/34 = about -0.8575

secT = 1/cosT = 5/3 = 1.666...