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

Answer:

we have

secθ = 2

$\frac{1}{cos θ}$=2

Cosθ =$\frac{1}{2 }$

$\frac{b}{h }=\frac{1}{2 }$

b=1

h=2

p=$\sqrt{2²-1} = \sqrt{3}$

again

Cot θ=$\frac{b}{p }$

Cot θ=$\frac{1}{ \sqrt{3}}$

Cot θ=$\frac{\sqrt{3}}{3}$

It lies in Quadrant III cot is positive

Cot θ=$\frac{\sqrt{3}}{3}$

b. (sqrt 3)/3