Question

Sec titha is 15/12 find the rest value

Answer 1

Given:

• The value of sec∅ is 15/12.

To Find:

• The values of rest trigonometric functions.

Answer:

Given that sec∅ = 15/ 12

Let the given ratio be 15x:12x.

And sec∅ = hypotenuse/base = BC/AB .

Now let us consider a right angled ∆ in which

• AB = 12 x
• BC = 15x .

So we must find , AC in order to find other ratios.

Now , in ∆ ABC ,

$\sf{\implies AC^{2}+AB^2=BC^2}$

$\sf{\implies AC^2 = BC^2-AB^2}$

$\sf{\implies AC ^2= (15x)^2-(12x)^2}$

$\sf{\implies AC^2=225x^2-144x^2}$

$\sf{\implies AC^2 = 81x^2}$

$\bf{\leadsto AC= 9x}$

And ,

• sin∅ = perpendicular/hypotenuse
• tan∅ = perpendicular/base
• cos∅ = base/hypotenuse

Also cosec∅ = 1/sin∅ and cot∅ = 1/tan∅

Hence ,

sin∅ = 9x/15x=9/15

tan∅ = 9x/12x =9/12

cos∅ = 12x/15x =12/15

cosec∅ = 15/9

cot∅ = 12/9