Question

If cot(theta)= 4/3, find csc(theta) (Picture provided)

Answer 1

The correct answer is option d

Explanation:

Trigonometric ratio

Cot θ = Adjacent side/Opposite side

It is given that,

Cot θ = 4/3

Adjacent side = 4

Opposite side = 3

Csc θ = Hypotenuse/Opposite side

To find the Hypotenuse

Hypotenuse² = Opposite side² + Adjacent side ² = 3²+ 4²

Hypotenuse = √(3²+ 4²) = 5

To find Csc θ

Csc θ = Hypotenuse/Opposite side = 5/3

The correct answer is option d

Csc θ = 5/3

Answer 2

D

Explanation:

If
`\cot \theta=(4)/(3),` then we can consider right triangle with adjacent leg 4 un. and opposite leg 3 un.. By the Pythagorean theorem,

`\text{hypotenuse}^2=\text{adjacent leg}^2+\text{opposite leg}^2,\\ \\\text{hypotenuse}^2=4^2+3^2,\\ \\\text{hypotenuse}^2=16+9,\\ \\\text{hypotenuse}^2=25,\\ \\\text{hypotenuse}=5\ un.`

So,

`\csc \theta=\frac{\text{hypotenuse}}{\text{opposite leg}}=(5)/(3).`