Deriviation behind trigonometric equationIn an example of a trigonometry book I'm reading, I see the following operations performed on this equation r = ( r + 3 ) cos ⁡ 2.23 ∘ : r = 3 cos ⁡ 2.23 ∘ + r cos ⁡ 2.23 ∘ r − r cos ⁡ 2.23 = 3 cos ⁡ 2.23 ∘ r = ( 3 cos ⁡ 2.23 ∘ 1 − cos ⁡ 2.23 ∘ ) Where r is the radius of a circle. The problem is that I can't understand how the second line in the above operations goes to the third. Can someone explain this to me?

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Deriviation behind trigonometric equationIn an example of a trigonometry book I&#039;m reading, I see the following operations performed on this equation   r  =  (  r  +  3  )  cos  ⁡      2.23    ∘  :            r  =  3  cos  ⁡      2.23    ∘    +  r  cos  ⁡      2.23    ∘              r  −  r  cos  ⁡  2.23  =  3  cos  ⁡      2.23    ∘              r  =      (                  3        cos        ⁡                  2.23          ∘                            1        −        cos        ⁡                  2.23          ∘                      )            Where r is the radius of a circle. The problem is that I can&#039;t understand how the second line in the above operations goes to the third. Can someone explain this to me?

dilettato5t1 · Accepted Answer

In the second line you have,  r  −  r  cos  ⁡  (  2.23  )  =  3  cos  ⁡  (  2.23  )Factor out an r from the left hand side,  r  (  1  −  cos  ⁡  (  2.23  )  )  =  3  cos  ⁡  (  2.23  )Then divide both sides by   (  1  −  cos  ⁡  (  2.23  )  ) Hope that helps!

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