if , acosα+bcosβ=Acos∅ proof that asinα+bsinβ=Asin∅


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Question Number 137864 by n0y0n last updated on 07/Apr/21

$if,$ $acos α + bcos β = Acos \emptyset$ $proof that$ $asin α + bsin β = Asin \emptyset$
Commented by mr W last updated on 07/Apr/21

$o n e {c a n}^{'} t p r o v e s o m e t h i n g w h i c h i s$ $w r o n g .$
Commented by n0y0n last updated on 07/Apr/21

Commented by mr W last updated on 07/Apr/21

$t h i s i s n o t t h e s a m e a s y o u r q u e s t i o n!$ $y o u r q u e s t i o n i s :$ $i f acos α + bcos β = Acos \emptyset$ $t h e n asin α + bsin β = Asin \emptyset$ $f o r a n y a, b, A, α, β, ϕ .$
Commented by mr W last updated on 07/Apr/21

$y o u s h o u l d m e a n t h a t c o n s t a n t$ $acos α + bcos β c a n b e e x p r e s s e d a s A \cos ϕ$ $a n d c o n s t a n t$ $asin α + bsin β c a n b e e x p r e s s e d a s A \sin ϕ .$ $t h i s i s t r u e .$ $g e n e r a l l y a n y t w o c o n s t a n t s, s a y p$ $a n d q, c a n b e e x p r e s s e d a s$ $p = A \cos ϕ$ $q = A \sin ϕ$ $w i t h A = \sqrt{p^{2} + q^{2}}$ $ϕ = \tan^{- 1} \frac{q}{p}$
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