Question

If secant theta equals 25/24 find cotangent theta

Answer 1

cotθ =
`(24)/(7)`

Explanation:

Secant of an angle is given as

secθ =
`(1)/(cos\theta)`

since cosθ =
`\frac{\text{Base}}{\text{Hypotenuse}}`

So secθ =
`\frac{\text{Hypotenuse}}{\text{Base}}` =
`(25)/(24)`

Now we have to find the value of cotθ

Since cotθ =
`\frac{\text{Base}}{\text{Height}}`

Now we'll find the height by Pythagoras theorem

Hypotenuse² = Base² + Height²

25² = 24² + Height²

625 = 576 + Height²

Height² = 625 - 576

= 49

Height = √49

= 7

Therefore, cotθ =
`(24)/(7)`

Answer 2

First we have to find the measurement of the missing leg because cotangent of an angle is the adjacent leg divided by the opposite leg. We do this by using Pythagorean Theorem. Let x = missing leg.

x² + 24² = 25²
x² + 576 = 625
x² = 625 - 576
x² = 49
x = 7

Our leg opposite of θ is 7 units long.

Secant is the hypotenuse divided by the adjacent leg. So if sec θ = 25/24, our adjacent leg is 24 units long.

Going back to what I said, cotangent is adjacent over opposite; which means cotangent of θ = 24/7 or ≈ 3.43