<p>What is the amplitude of the graph of y = a<em>cosx + b</em>sinx?</p>
<p>I know the answer is sqroot of (a^2 + b^2), but does anyone actually understand the explanation?</p>
<p>You just take it how it is.</p>
<p>Anybody know what the amplitude of sinx + x is?</p>
<p>If you've payed mor attention on your trig class you would know the answer :P</p>
<p>just kiding, ok listen:</p>
<p>f(x)=a<em>sin(x)+b</em>cos(x)=(sqrt(a^2+b^2))*sin(x+someangle)</p>
<p>where tan(someangle)=b/a</p>
<p>so you get a function which that look like this f(x)=m*sin(x+someanlge) where m is the amplitude you need :P</p>
<p>it's just a way in trig of converting a<em>sinx+b</em>cosx in to a sine function.. there is a proof, and it's quick one, but i'm not really willing to write it....</p>
<p>As for sinx + x i'm not sure there is an amplitude...? cause... well, no matter that sinx goes from -1 to 1, x stretches to infinity :P</p>
<p>either no or infinite amplitude.
or symbolically, the amplitude will be 1+x (amplitude of sin(x) + 'amplitude' of x).</p>