Question

If tan θ=3\4 , find csc

Answer 1

In a rectangular triangle $\tan\theta\dfrac{opposite}{adjacent}$.

We have $\tan\theta=\dfrac{3}{4}$

Therefore opposite = 3uints and adjacent = 4units.

$\csc\theta=\dfrac{hypotenuse}{opposite}$

We need the length of hypotenuse.

Use the Pythagorean theorem:

$h^2=3^2+4^2\\\\h^2=9+16\\\\h^2=25\to h=\sqrt{25}\to h=5units$

Substitute:

$\csc\theta=\dfrac{5}{3}$