Question

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

Answer 1

Answer:

D

Step-by-step explanation:

If $\cot \theta=\dfrac{4}{3},$ 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,

$\csc \theta=\dfrac{\text{hypotenuse}}{\text{opposite leg}}=\dfrac{5}{3}.$

Answer 2

Answer:

The correct answer is option d

Step-by-step 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