SOLUTION: 1. Express 3cos(x°)+5sin(x°) in the form kcos(x°-a°), where k>0 and 0≤a≤360 Can you provide full working with the solutions please. Many Thanks, Andrew.

Draw a right triangle with those coefficients as legs:

horizontal leg = 3 and vertical leg = 5

 

Calculate the hypotenuse using the Pythagorean theorem







 

 so 

 so 

Substitute  for 3 and
substitute  for 5 in


 =

 =

factor out  on the left side:

 =

Now we remember the formula , and the above can be written:

 =



Since , the above becomes:








This is in the form  

where  and 
 
So we have

 =  = 

Edwin