Question

Evaluate cos⁻¹ [cos $\frac{5\pi}{4}$]

Answer 1

Hi,

⇒   " 5π/4 " is the answer to this Question.

Solution:

There are two functions in the statement of this question.

Both the functions are Trigonometric Functions.

⇒ cos is a Trigonometric function.

⇒ And cos⁻¹ is an Inverse Trigonometric Function.

   It is the inverse of the cos function.

We have given that  

cos⁻¹[cos 5π/4]

So both the functions will cancel each other and we get the answer which is

 " 5π/4 "

⇒ I Hope that it will help you.

Answer 2

Answer:

cos⁻¹ (cos 5π/4)=3π/4

Step-by-step explanation:

To find the value of

$cos^{-1}(cos\:\frac{5\pi }{4})$

since cos⁻¹ cancels cos only if 5π/4 lies between principal value branch[0,π]

cos(5π/4)=cos(2π-3π/4)

=> cos(3π/4)         ∵since cos(2π-θ)=cos θ

=> cos⁻¹[cos(3π/4)]   here 3π/4 belongs to  [0,π](lies between 0 to π)

so

=> 3π/4

cos⁻¹ (cos 5π/4)=3π/4

hope it helps you.