Question

Determine the exact value of
`\csc(0)`when
`\cot(0) = 3 / 4`and
`\cos(0) \ \textgreater \ 0`

Answer 1

The cot(θ) is given by:

`\cot (\theta)=(adjacent)/(opposite)=(3)/(4)`

so:

The hypotenuse can be found using pythagorean theorem:

`\begin{gathered} x=\sqrt[]{4^2+3^2} \\ x=\sqrt[]{25} \\ x=5 \end{gathered}`

Therefore, the csc(θ) is given by:

`\begin{gathered} \csc (\theta)=(hypotenuse)/(opposite) \\ so\colon \\ \csc (\theta)=(5)/(4) \end{gathered}`