Homework Help

Why cos(-x)=cosx?Explain,please.

user profile pic

sokolof | Student, Grade 11 | (Level 2) eNoter

Posted August 18, 2011 at 12:43 AM via web

dislike 1 like

Why cos(-x)=cosx?Explain,please.

2 Answers | Add Yours

user profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted August 18, 2011 at 12:45 AM (Answer #1)

dislike 0 like

We can write cos (-x) = cos (0-x), such as the following identity may now be used:

cos (a-b) = cos a*cos b + sin a*sin b

Let a = 0 and b = x

cos (0-x) = cos 0*cos x + sin 0*sin x

But cos 0 = 1 and sin 0 = 0.

cos (0 - x) = 1*cos x + 0*sin x

cos (0 - x) = cos x

Therefore, the identity cos(-x) = cos x is verified.

user profile pic

boominathan | eNotes Newbie

Posted April 20, 2015 at 4:08 PM (Answer #2)

dislike 0 like

Hi,

A geometric explanation is very intutive.

Look at sin(x) curve below. Sin(-1) = -Sin(1). it is not symmetric

But look at the cos(x) curve below. cos(-1) = cos(1). it is symmetric

Join to answer this question

Join a community of thousands of dedicated teachers and students.

Join eNotes