Question

Find cotθ if θ terminates in Quadrant III and secθ = 2

a. - (sqrt 3)/3
b. (sqrt 3)/3
c. - sqrt 3
d. sqrt 3

Answer 1

we have

secθ = 2

`(1)/(cos θ)`=2

Cosθ =
`(1)/(2 )`

`(b)/(h )=(1)/(2 )`

b=1

h=2

p=
`√(2²-1) = √(3)`

again

Cot θ=
`(b)/(p )`

Cot θ=
`(1)/( √(3))`

Cot θ=
`(√(3))/(3)`

It lies in Quadrant III cot is positive

Cot θ=
`(√(3))/(3)`

b. (sqrt 3)/3