Question

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

Answer 1

The correct answer is option b

Cot θ = 24/7

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

Answer 2

B

Explanation:

By the definition,

`\sec \theta=\frac{\text{hypotenuse}}{\text{adjacent leg}}.`

If
`\sec \theta=(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=\frac{\text{adjacent leg}}{\text{opposite leg}}=(24)/(7).`