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

Algebra.Com
Question 348596: 21cos(x) + 20 sin(x) can be written in the form Asin(x+ b) where A>0 and
-pi < b < pi
Thanks already!

Answer by Edwin McCravy(20081)   (Show Source): You can put this solution on YOUR website!
can be written in the form where A>0 and
Cheers in advance
Assume:





Let 









--------------------------------------
Now go back to:



And now let 









-------------------------

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

RELATED QUESTIONS

21cos(x)+20sin(x) can be written in the form Asin(x+b) where A>0 and -pi (answered by Edwin McCravy)
Find all solutions of each of the equations in the interval [0,2pi). a)... (answered by KMST)
express in the form a+bi, where a and b are real numbers. 7(cos pi+ i sin... (answered by Fombitz)
If sin x = {{{12/13}}} where {{{pi/2 <= x <= pi}}}, determine: a) {{{sin (x/2)}}}... (answered by lwsshak3)
Could someone help me with this problem. g(x)=1-sin^(2)X where x is in radians the... (answered by stanbon)
Find all solutions to the equation sin x = 0. a. x = {{{PI}}}n b. x = 2{{{PI}}}n c. x... (answered by bucky)
Rewrite −3sin(x)−1cos(x) as Asin(x+ϕ)? A: ϕ: When -pi <... (answered by Fombitz)
Consider the function g(x)=sin(x-(pi/4)). Which expression gives the values of the... (answered by Fombitz)
Find all solutions in the interval [0,2PI] to the equation {{{cos^(2)(x=1)}}}. a. x = 0, (answered by jim_thompson5910,ffc_01)