Question

Given that sec 0= -37/12, what is the value of cot 0, for pi/2 < 0 pi?

Answer 1

`-(12)/(35)`

Explanation:

Given,

`sec\theta = -(37)/(12)`

We know that,

`sec \theta = (H)/(B)`

Where, H is the hypotenuse of a right triangle and B is its base,

By making diagram,

By applying pythagoras theorem,

The Perpendicular of the triangle,

`P=√(H^2-B^2)=√(37^2-12^2)=√(1369-144)=√(1225)=35`

Hence,
`cot \theta = -(B)/(P)=-(12)/(35)`

( We took the negative sign because
`(\pi)/(2)< \theta < \pi` )

Answer 2

cot(θ) = -12/35

Explanation:

cot(θ) = -1/√(sec(θ)^2 -1) . . . . negative in the second quadrant

= -1/√((-37/12)^2 -1) = -1/(35/12)

cot(θ) = -12/35