Question

If tan θ=3\4 , find csc

Answer 1

In a rectangular triangle
`\tan\theta(opposite)/(adjacent)`.

We have
`\tan\theta=(3)/(4)`

Therefore opposite = 3uints and adjacent = 4units.

`\csc\theta=(hypotenuse)/(opposite)`

We need the length of hypotenuse.

Use the Pythagorean theorem:

`h^2=3^2+4^2\\\\h^2=9+16\\\\h^2=25\to h=√(25)\to h=5units`

Substitute:

`\csc\theta=(5)/(3)`