Question

What is csc Ø when cot Ø =3? (Rationalize the denominator if necessary)

Answer 1

`√(10)`

Explanation:

Using the Pythagorean identity

sin²x + cos²x = 1 ( divide all terms by sin²x )

1 +
`(cos^2x)/(sin^2x)` =
`(1)/(sin^2x)`

1 + cot²x = csc²x

When cotΘ = 3, then

1 + 3² = csc²Θ

csc²Θ = 10 ( take the square root of both sides )

cscΘ =
`√(10)`