Calculating components of a third-quadrant vector

[Joe_mama69]

Homework Statement

I am not sure if I did this right as it wasn't as complicated as I think the solution should be and I couldn't find anything online as to how the solution is even supposed to look like. I inserted an imgur link of my answer in case the image on here isn't clear: https://imgur.com/a/tE28WWu

Calculate the components of a third quadrant vector C in the following ways:

1. use the angle between the vector and the negative x-axis (delta) and apply right-triangle trigonometry

2. use the angle between the vector and the negative y-axis (epsilon) and apply right-triangle trigonometry

3. use the standard angle for the vector (gamma) - that is, find the connection between gamma and delta in the formulas you found in part 1.

4. use the standard angle for the vector (gamma) - that is, find the connection between gamma and epsilon in the formulas you found in part 2.

Relevant Equations

x component = magnitude * cos(standard angle)
y component = magnitude * sin(standard angle)

 

[Tomy World]

1) Correct

2) Wrong. Check yr answer again!

3) What are the generic rules for below:
sin(π + θ) = ?
cos(π + θ) = ?

Apply above result to below to see relation with 1.
Cy = C sin(ϒ) = C sin(π + δ) = ?
Cx = C cos(ϒ) = C cos(π + δ) = ?

4) What are the generic rules for
sin(2π + θ) = ?
cos(2π + θ) = ?
cos(- θ) = ?
sin(- θ) = ?
cos(π/2 + θ) = ?
sin(π/2 + θ) = ?

Apply them to below to see the relation with 2.
Cy = C sin(ϒ) = C sin(3π/2 - ϵ) = C sin(2π – (π/2 + ϵ)) = ?
Cx = C cos(ϒ) = C cos(3π/2 - ϵ) = C cos(2π – (π/2 + ϵ)) = ?

 

[Joe_mama69]

1) Correct

2) Wrong. Check yr answer again!

3) What are the generic rules for below:
sin(π + θ) = ?
cos(π + θ) = ?

Apply above result to below to see relation with 1.
Cy = C sin(ϒ) = C sin(π + δ) = ?
Cx = C cos(ϒ) = C cos(π + δ) = ?

4) What are the generic rules for
sin(2π + θ) = ?
cos(2π + θ) = ?
cos(- θ) = ?
sin(- θ) = ?
cos(π/2 + θ) = ?
sin(π/2 + θ) = ?

Apply them to below to see the relation with 2.
Cy = C sin(ϒ) = C sin(3π/2 - ϵ) = C sin(2π – (π/2 + ϵ)) = ?
Cx = C cos(ϒ) = C cos(3π/2 - ϵ) = C cos(2π – (π/2 + ϵ)) = ?

Thanks I've got it now!