Question

Question #0280a

Answer 1

`sin(theta) = (6sqrt52)/52`, `cos(theta) = (-4sqrt52)/52`, `sec(theta) = -sqrt52/4`, `csc = sqrt(52)/6` and `cot(theta) = -4/6`

Explanation:

The cotangent is the reciprocal of the tangent:

`cot(theta) = -4/6`

Use `1 + tan^2(theta) = sec^2(theta)` to obtain the secant and the cosine; we know that both the secant and the cosine must be negative because we are given `sin(theta) > 0`

`1 + ((-6)/4)^2 = sec^2(theta)`

`sec^2(theta) = 16/16 + 36/16`

`sec^2(theta) = 52/16`

`sec(theta) = -sqrt52/4`

`cos(theta) = (-4sqrt52)/52`

`sin(theta) = (-6/4)cos(theta)`

`sin(theta) = (6sqrt52)/52`

`csc = sqrt(52)/6`