Question

If cot0 =4/3 find csc0

Answer 1

`\mathrm{d. \csc \theta =(5)/(3)}`

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 =(4)/(3)` as given in the problem, then
`\tan \theta =(3)/(4)`, because
`\tan \theta =(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=√(4^2+3^2)=√(25)=5`.

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

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

`\csc \theta=(1)/(\sin \theta)=(1)/((3)/(5))=\boxed{(5)/(3)}`