Can y(x)=a*sin(kx)+b*cos(kx) presented simpler?

[finsener]

Hi!

i wonder if it's possible to present y(x)=a*sin(kx)+b*cos(kx) as one function like y(x)=A*sin(kx+c) where A and c are constants?

 

[Hurkyl]

Sure is. Try using the addition of angle formula on A*sin(kx+c) and see if you can figure out how!

 

[himanshu121]

substitue $$a= \sqrt{a^2+b^2} * cos \theta$$
and $$b= \sqrt{a^2+b^2} * sin \theta$$

now
u can see that

A= $$\sqrt{a^2+b^2}$$

and c= $$\theta = \arctan {\frac{b}{a}}$$