Trigonometric functions help please?

cot(θ) = cos(θ)/sin(θ)

θ lies in the second and third quadrant. when θ=pi, cot(θ) is undefined

sin(pi)=0

cos(pi)=-1

tan(pi) = sin(pi)/cos(pi) = 0

sec(pi) = 1/cos(pi) = -1

csc(pi) = 1/sin(pi) = 1/0 = undefined

cot(pi) = cos(pi) / 0 = undefined

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θ = 10pi/3

10pi/3 = 3pi + pi/3 = 2pi + (pi+pi/3) = 2pi+4pi/3 = 4pi/3 = pi+pi/3

θhe reference angle is pi/3 and θ lies in quadrant 3

sin(10pi/3) = sin(pi/3) = -*3/2 (sine is negative in quadrant III)

cos(10pi/3) = cos(pi/3) = -1/2 (cos is negative in quadrant III)

tan(10pi/3) = sin(pi/3) / cos(pi/3) = *3

cot(10pi/3) = 1/tan(pi/3) = 1/*3

csc(10pi/3) = 1/sin(pi/3) = -2 /*3

sec(10pi/3)= 1/cos(pi/3) = -2

cotθ = cosθ/sinθ

If cotθ is undefined, then sinθ = 0

arcsin(0) = 0, π, 2π, ...

π/2 ≤ θ ≤ 3π/2

θ = π

:::::

θ = 10π/3

θ' = 4π/3

sinθ' = -√3/2

cosθ' = -1/2

tanθ' = √3

you can do the rest

(t for theta)

cot(t) undefined at t= npi and pi/2=< t =< 3pi/2

---> t=pi