Question

If cos theta = 12/13 then what is the value of tan theta

Answer 1

The  value of tanθ = 5/12.

Explanation:

Given, cosθ = 12/13

By Trigonometry , cosθ = Base / Hypotenuse

Comparing it with cosθ = 12/13  , we get Base = 12  and         Hypotenuse = 13.

We will construct a triangle with a base 12 and hypotenuse 13 .

By Pythagorean theorem ,

(Hypotenuse)²  = (Perpendicular)² + (Base)²

(13)² = (Perpendicular)² + (12)²

169 - 144 = (Perpendicular)²

(Perpendicular)² = 25

Perpendicular = 5

WKT,

tanθ = Perpendicular / Base

(or)

tanθ = Opposite / Adjacent

= 5/12

(Here perpendicular means adjacent)

Hence, value of tanθ = 5/12.

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Answer 2

Answer:

The value of tanθ = 5/12

Step-by-step explanation:

Given the value of

$cos\theta = \dfrac{12}{13}$

In a triangle, the trigonometric ratio cosθ, is given by

$cos\theta = \dfrac{adjacent}{hypotenuse}$

Comparing this with the given value, the length of the adjacent side is 12  units and of hypotenuse is 13units.

Applying Pythagoras theorem,

$(\mbox{hypotenuse})^2 = (\mbox{opposite~side})^2 + (\mbox{adjacent})^2$

$\implies (13)^2 = (\mbox{opposite~side})^2 + (12)^2$

$\implies(\mbox{opposite~side})^2 = 169 - 144=25$

$\implies\mbox{opposite~side} = \sqrt{25} =5\mbox{units}$

In a triangle, the trigonometric ratio tanθ, is given by

$\mbox{tan}\theta = \dfrac{\mbox{oppsoite side}}{\mbox{adjacent side}}$

Substituting the values,

$\mbox{tan}\theta = \dfrac{5}{12}$

Hence, the value of tanθ = 5/12.

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