$Sinusoidal function question help$

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$Sinusoidal function question help$

The graph of 𝑦 = 3cos(2(𝑥 +12°)) - 5 is the same as the graph of 𝑦 = 3sin(2(𝑥 +G°)) -5. State 2 values of G. Show steps.

Functions Trigonometric Functions

Boil Dwasd

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We have
\[𝑦 = 3\cos(2(𝑥 +12°)) - 5=3\sin(2(𝑥 +G°)) -5\]
\[\Rightarrow 3\cos(2(𝑥 +12°))= 3\sin(2(𝑥 +G°))\]
\[\Rightarrow \cos(2(𝑥 +12°))= \sin(2(𝑥 +G°))=\cos (90- 2(𝑥 +G°))\]
\[\Rightarrow \cos(2(𝑥 +12°))= \cos (90- 2(𝑥 +G°))\]
\[\Rightarrow \cos(2x +24°)= \cos (90- 2𝑥 -2G°))\]
\[\Rightarrow 2x +24°= 360k \pm (90- 2𝑥 -2G°) (1)\]
for any integer $k$ and for every $x$. Since (1) holds for all values of $x$, the coefficient of $x$ should be the same on both sides. Thus

\[\Rightarrow 2x +24°= 360k - (90- 2𝑥 -2G°) \]
\[\Rightarrow 24= 360k-90+2G \]
\[\Rightarrow 24+90-360k= 2G \]
\[\Rightarrow G=12+45-180k=57-180k. \]
So
\[\Rightarrow G=57-180k. \]
You can choose $k$ anything you like. Letting $k=0$ we get $G=57$, and letting $k=-1$ we get $G=237$.

Erdos

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$Sinusoidal function question help$

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