Question

If sin theta =12/13, then find the value of tan theta and sec theta

Answer 1

hope this answer helps you

Answer 2

The value of tanθ is 12/5 and the value of secθ is 13/5

Given : Value of sinθ is 12/13

To find : Value of tanθ and secθ

Solution :

We can simply solve this mathematical problem by using the following mathematical process. (our goal is to calculate the values of tanθ and secθ)

Here, we will be using general trigonometric formula.

Now, w.r.t to a right angled angle, we know that :

sinθ = perpendicular/hypotenuse

As,

sinθ = 12/13

So,

perpendicular/hypotenuse = 12/13

Which implies,

• perpendicular = 12
• hypotenuse = 13

Let, the base of the right angled triangle = x

Applying Pythagoras theorem,

(12)² + (x)² = (13)²

x² = 169-144

x² = 25

x = √25

x = 5

So, in the associated right angled triangle :

• perpendicular = 12
• hypotenuse = 13
• base = 5

Now,

tanθ = perpendicular/base = 12/5

And,

secθ = hypotenuse/base = 13/5

Hence, the value of tanθ is 12/5 and the value of secθ is 13/5