Question

Convert the following polar-form vectors of the form ⟨r,θ⟩ into component-form vectors of the form ⟨x,y⟩. Your answers should be in the form "< #, # >". ⟨13,50∘⟩=   ⟨1.77,250∘⟩=    ⟨5.8,150∘⟩= ​

Answer 1

9514 1404 393

Answer:

  a) <8.356, 9.959>

  b) <-0.605, -1.663>

  c) <-5.023, 2.9>

Step-by-step explanation:

Many calculators can perform polar ⇔ rectangular conversion. Attached is the result from one of them. Of course, you can also program a spreadsheet to do it. (The ATAN2( ) function is useful for finding the correct angle.)

If you want to do these calculations by hand, the conversion is ...

  <r, θ> ⇒ <r·cos(θ), r·sin(θ)>

In the attached, the rectangular coordinates are shown as complex numbers. The imaginary component is the y-component of the vector.