About velocity equation in simple harmonic motion

[Thaurron]

Homework Statement

Actually this is not a problem. This is about something i couldn't understand.

Homework Equations

where wt equals θ

The Attempt at a Solution

I can understand that x=r.cosθ it is obvious. But i can't understand why Vx=-V.sin(w.t) When i take a triangle from that circle i end up finding Vx equal to V.sin(w.t) . Where do we get that minus? Also how does he find the angle as 90+wt in that equation? I think it should be 90 - wt

Note: I don't want the explanation with derivative.

 

[haruspex]

how does he find the angle as 90+wt in that equation?

It's all there in the diagram. The angle from the +ve X axis anticlockwise around to the velocity vector is shown as 90+theta. If that's not clear, project the blue radius line through the particle to cut the angle into two parts.

 

[Thaurron]

Ummm.. I think i couldn't express my problem. I can understand why is that angle is 90 + theta. My problem is different.

If you take triangle which has a pink vector leftward and green vector which making an angle of alpha with the pink vector (where alpha is 90 - theta) and put the Vy component into the emptry section of that triangle you will see that Vx equals V.cos(alpha) which is 90 - theta so equation becomes Vx=V.cos(90-theta)

As i know, that 90 degree in the cosinus will turn it into a sinus but won't add a minus to it since 90 - theta is in the first section of coordinate system.

Summary: My problem is with that minus... Btw thank you for helping.

 

[haruspex]

If you take triangle which has a pink vector leftward and green vector which making an angle of alpha with the pink vector (where alpha is 90 - theta) and put the Vy component into the emptry section of that triangle you will see that Vx equals V.cos(alpha) which is 90 - theta so equation becomes Vx=V.cos(90-theta)

But in that diagram you have drawn Vx as a left-pointing vector. Since right is positive, you should take Vx as right-pointing. You then see that it is Vcos(90+theta), hence the minus sign.

 

[Thaurron]

Got it. Thanks a lot.