Problem: create the basis (f1,f2) by rotating

The orthonormal basis vectors by the

Angle 3pi/4 in r^2. We have basis e aswell as

Standard,basis

Ok im on My iphone unable to draw any picture

But imagine urself with (e1,e2)

E1 is pointing in x direction and e2 pointing straight

Up on y

I Will get to My question soon.

Ok we create another basis f1,f2 and rotate

It 3pi/4

I guess now F1 is pointing 135 degrees and

F2 will get onto 225 degrees, correct me

If i think wrong

According to the answer

We get this:

F1= -e1*cos 3pi/4 + e2*sin 3pi/4

F2= -e1*sin 3pi/4 - e2*cos 3pi/4

I understand nothing of this

I would likeTo know how they picked

Cos,sine for f1 and how they chose

Sin,cos for f2, how should one think

When it comes to vectors? Is there any

General rule I should think of while selecting

The trig functions

Uhmm I completed calculus a while back, but

I have pretty bad skills in trig

Hope someone can figure it out