Question

If sec(theta) =25/24, find cot(theta) (Picture provided)

Answer 1

Answer:

B

Step-by-step explanation:

By the definition,

$\sec \theta=\dfrac{\text{hypotenuse}}{\text{adjacent leg}}.$

If $\sec \theta=\dfrac{25}{24},$ we can consider right triangle with hypotenuse 25 un. and adjacent leg 24 un. By the Pythagorean theorem,

$\text{hypotenuse}^2=\text{adjacent leg}^2+\text{opposite leg}^2,\\ \\\text{opposite leg}^2=25^2-24^2,\\ \\\text{opposite leg}^2=625-576,\\ \\\text{opposite leg}^2=49,\\ \\\text{opposite leg}=7\ un.$

So,

$\cot \theta=\dfrac{\text{adjacent leg}}{\text{opposite leg}}=\dfrac{24}{7}.$

Answer 2

Answer:

The correct answer is option b

Cot θ  = 24/7

Step-by-step explanation:

Sec θ = Hypotenuse/Adjacent side

Cot θ = Adjacent side/Opposite side

It is given that,

secθ = 25/24

Hypotenuse =25

Adjacent side = 24

To find opposite side

Opposite side of θ = √(25² -  24²) = √625 - 576 = 7

To find cot θ  

Cot θ = Adjacent side/Opposite side = 24/7

Therefore the correct answer is option b

Cot θ = 24/7