Question

If sin theta = root 6 then find the value of cos theta and tan theta

Answer 1

Answer:

cos theta = √7

tan theta = √6 / √7

Step-by-step explanation:

Given,

sin theta = √6

We know that, Trigonometry is applied in the right triangles. Thus the given triangle is right angled triangle.

And,

sin theta = Perpendicular / Hypotenuse

Also, sin theta = √6 = √6/1

Then,

We get,

Perpendicular /Hypotenuse = √6/1

So, let Perpendicular = x√6 and Hypotenuse = 1x, where x is the constant by which both 1 and √6 is multiplied.

Now, applying Pythagoras theorem, we get,

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

=> (1x)^2 = (x√6)^2 + (Base)^2

=> x^2 = 6x^2 + (Base)^2

=> (Base)^2 = 7x^2

=> Base = √7x^2 = x√7

Now,

Cos theta = Base/Hypotenuse =

x√7 / 1x = √7 / 1 = √7

Tan theta = Perpendicular/Base =

x√6 / x√7 = √6 / √7