SOLUTION: 21cos(x) + 20 sin(x) can be written in the form Asin(x+ b) where A>0 and -pi < b < pi Thanks already!

Assume:





Let 









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Now go back to:



And now let 









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So we have this system of equations:



Dividing equals by equals:









 


Draw a right triangle with horizontal leg 20 and vertical leg 21,
so the angle at the bottom left will have tangent , and
therefore be equal to b. 

 and by the Pythagorean theorem 

Since













Therefore   and 

and:




Edwin