SOLUTION: By expanding cos(x-60), express 7cos(X) + 8cos(x-60) in the form Rsin(x+y),where R>0 and y is acute. I expanded cos(x-60) using an identity and got cos(x)cos60+sin(x)sin60 but the

Algebra ->  Trigonometry-basics -> SOLUTION: By expanding cos(x-60), express 7cos(X) + 8cos(x-60) in the form Rsin(x+y),where R>0 and y is acute. I expanded cos(x-60) using an identity and got cos(x)cos60+sin(x)sin60 but the      Log On


   



Question 1048799: By expanding cos(x-60), express 7cos(X) + 8cos(x-60) in the form Rsin(x+y),where R>0 and y is acute.
I expanded cos(x-60) using an identity and got cos(x)cos60+sin(x)sin60 but then couldn't understand how to express that in the form Rsin(x+y).

Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
7cos%28x%29+%2B+8cos%28x-%2260%B0%22%29%22%22=%22%22

%22%22=%22%22

7cos%28x%29+%2B+8%28cos%28x%29%5E%22%22%281%2F2%29+%2B+sin%28x%29%28sqrt%283%29%2F2%29%29%29%22%22=%22%22

7cos%28x%29+%2B+4cos%28x%29+%2B+4sqrt%283%29sin%28x%29%22%22=%22%22

11cos%28x%29+%2B+4sqrt%283%29sin%28x%29

Draw a right triangle with opposite side 11 and adjacent
side 4sqrt%283%29, and angle y

 

Then 

 

And +y=arctan%2811%2F%284sqrt%283%29%29%29+=+%2257.79577249%B0%22

11%2F13=sin%28y%29, 4sqrt%283%29%2F13=cos%28y%29

11=13%2Asin%28y%29, 4sqrt%283%29=13%2Acos%28y%29

Substitute for 11 and 4sqrt%283%29 in

11cos%28x%29+%2B+4sqrt%283%29sin%28x%29%22%22=%22%22

13%2Asin%28y%29cos%28x%29+%2B+13%2Acos%28y%29sin%28x%29%22%22=%22%22

13%28sin%28y%29cos%28x%29%5E%22%22+%2B+cos%28y%29sin%28x%29%29%22%22=%22%22

13%28sin%28y%2Bx%29%5E%22%22%29%22%22=%22%22

13sin%28x%2By%29%29%22%22=%22%22

13sin%28x%2B%2257.79577249%B0%22%29%29
 
Edwin