Question

Find cotθ, sinθ, and cscθ, where θ is the angle shown in the figure.Give exact values, not decimal approximations.

Answer 1

In the given right triangle

Applying the Pythagorean Theorem

Find out the vertical leg (y)

`\begin{gathered} 8^2=3^2+y^2 \\ y^2=8^2-3^2 \\ y^2=55 \\ y=√(55) \end{gathered}`

Find out the cotθ

`cotθ=(3)/(√(55))`

Simplify

`cotθ=(3√(55))/(55)`

Find out the sinθ

`sinθ=(√(55))/(8)\text{ ----> by SOH}`

Find out cscθ

cscθ=1/sinθ

`cscθ=(8)/(√(55))`

Simplify

`cscθ=(8√(55))/(55)`