Question

If cot0 =4/3 find csc0

Answer 1

Answer:

$\mathrm{d. \csc \theta =\frac{5}{3}}$

Step-by-step explanation:

In a right triangle only, the tangent of an angle is equal to its opposite side divided by its adjacent side. If $\cot\theta =\frac{4}{3}$ as given in the problem, then $\tan \theta =\frac{3}{4}$, because $\tan \theta =\frac{1}{\cot \theta}$. Therefore, the opposite side of angle theta is 3 and its adjacent side is 4. Thus, the hypotenuse of the triangle must be $h=\sqrt{4^2+3^2}=\sqrt{25}=5$.

The sine of an angle in a right triangle is equal to its opposite side divided by its hypotenuse.

Therefore, $\sin \theta =\frac{3}{5}$ (o/h) and since $\sin \theta =\frac{1}{\csc \theta}$, we have:

$\csc \theta=\frac{1}{\sin \theta}=\frac{1}{\frac{3}{5}}=\boxed{\frac{5}{3}}$