Let a , b , c &#x2208;<!-- ∈ --> [ 0 ; &#x03C0;<!

Anthony Kramer

Anthony Kramer

Answered question

2022-05-19

Let a , b , c [ 0 ; π 2 ] such that
cos a = a ; sin cos b = b ; cos sin c = c .
Put the numbers a,b,c in ascending order

Answer & Explanation

asafand2c

asafand2c

Beginner2022-05-20Added 11 answers

(1) Note that x is strictly increasing and cos x is strictly decreasing (in the range [ 0 , π 2 ]). So x < cos x iff x(2) We have sin x < x (for all x in the range [ 0 , π 2 ]), so sin c < c. But cos x is strictly decreasing, so c = cos sin c > cos c. Hence applying (1) we have c>a.
(3) sin x < x also implies b = sin cos b < cos b. So, again applying (1), we have bSummarising b

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?