how do I graph the function f(x)=sin(4x)-2cos(4x) in the calculator. find a, b and c so it is writtes a sinusoid for of f(x)= a sin (b(x-c) or acos(b(x-c)??????????

Question

how do I graph the function f(x)=sin(4x)-2cos(4x) in the calculator. find a, b and c so it is writtes a sinusoid for of f(x)= a sin (b(x-c)   or   acos(b(x-c)??????????

myininaya · Answer

$$f(x)=1\sin(4x)-2\cos(4x)=\frac{\sqrt{2^2+1^2}}{\sqrt{2^2+1^2}}(1 \sin(4x)-2 \cos(4x))$$
$$f(x)=\sqrt{4+1}(\frac{1}{\sqrt{4+1}} \sin(4x)-\frac{2}{\sqrt{4+1}} \cos(4x))$$
$$f(x)=\sqrt{5}(\frac{1}{\sqrt{5}}\sin(4x)-\frac{2}{\sqrt{5}}\cos(4x))$$
now the reason i wrote this is because i was thinking about labeling a right triangle like this
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