Can Someone Explain This Trig Picture to Me?

[Meadman23]

Main Question or Discussion Point

Its the attached picture. I'm not seeing why when using the dot product, they start using sin.

 

[SteamKing]

The picture is self explanatory. If you know trig, it should be elementary.

 

[UltrafastPED]

Projections onto different axes.

 

[Meadman23]

I'm just not getting it. '
I see that the angle between r and x is phi, thus in using the formula, r (dot) x = (1)(1) cos(phi).

Then I see the angle between r and y is (90-phi), thus in using the formula, r (dot) y = (1)(1)cos(90-phi) = sin (phi).

I then see the angle between phi and x is (90 +phi), thus in using the formula, phi (dot) x = (1)(1)cos(90+phi) = -sin (phi)

I then see the angle between phi and y is (180 - phi), thus in using the formula, phi (dot) y = (1)(1)cos(180-phi) = -cos (phi)???

I don't get why the last one is +cos(phi)....

 

[UltrafastPED]

Look at the blue part of the diagram ... phi(dot)y = cos(phi).