6.3.1 Write down the amplitude of $$ f $$. 6.3.2 Draw the graph of $$ g(x)=\cos \left(x-30^{\circ}\right) $$ for the interval $$ x \in\left[-150^{\circ} ; 210^{\circ}\right] $$ on the $$ g $$ g provided in the ANSWER BOOK. Clearly show ALL intercepts with the axes ar endpoint(s) of the graph. 6.3.3 Use the graphs to determine the values of $$ x $$, in the interval $$ x \in\left[-150^{\circ} ; 210^{\circ}\right] $$, which: (a) g(x)P$$ f(x) $$

Question

6.3.1 Write down the amplitude of $$ f $$. 6.3.2 Draw the graph of $$ g(x)=\cos \left(x-30^{\circ}\right) $$ for the interval $$ x \in\left[-150^{\circ} ; 210^{\circ}\right] $$ on the $$ g $$ g provided in the ANSWER BOOK. Clearly show ALL intercepts with the axes ar endpoint(s) of the graph. 6.3.3 Use the graphs to determine the values of $$ x $$, in the interval $$ x \in\left[-150^{\circ} ; 210^{\circ}\right] $$, which: (a) g(x)>>P$$ >f(x) $$

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### 6.3.1 Amplitude of $$ f $$

The amplitude of a function $$ f(x) $$ that is in the form of a sine or cosine function, such as $$ f(x) = A \sin(Bx + C) + D $$ or $$ f(x) = A \cos(Bx + C) + D $$, is given by the absolute value of $$ A $$.

Since the function $$ f $$ is not explicitly provided in the problem, I cannot determine the amplitude without knowing the specific form of $$ f $$. Please provide the function $$ f $$ to proceed with this part.

### 6.3.2 Graph of $$ g(x) = \cos(x - 30^{\circ}) $$

To graph $$ g(x) = \cos(x - 30^{\circ}) $$ over the interval $$ x \in [-150^{\circ}, 210^{\circ}] $$, we need to find the key points, including intercepts with the axes.

1. **Find the x-intercepts**: Set $$ g(x) = 0 $$:
   $$
   \cos(x - 30^{\circ}) = 0
   $$
   This occurs when:
   $$
   x - 30^{\circ} = 90^{\circ} + k \cdot 180^{\circ} \quad (k \in \mathbb{Z})
   $$
   Solving for $$ x $$:
   $$
   x = 120^{\circ} + k \cdot 180^{\circ}
   $$

For $$ k = -1 $$:
   $$
   x = -60^{\circ}
   $$
   For $$ k = 0 $$:
   $$
   x = 120^{\circ}
   $$
   For $$ k = 1 $$:
   $$
   x = 300^{\circ} \quad (\text{not in the interval})
   $$

Thus, the x-intercepts are at $$ x = -60^{\circ} $$ and $$ x = 120^{\circ} $$.

2. **Find the y-intercept**: Set $$ x = 0 $$:
   $$
   g(0) = \cos(0 - 30^{\circ}) = \cos(-30^{\circ}) = \frac{\sqrt{3}}{2}
   $$

3. **Key points**: The cosine function has a period of $$ 360^{\circ} $$. The function will complete one full cycle from $$ -150^{\circ} $$ to $$ 210^{\circ} $$.

Now, let's plot the graph of $$ g(x) $$ and mark the intercepts.

### 6.3.3 Determine values of $$ x $$ where $$ g(x) > f(x) $$

To find the values of $$ x $$ in the interval $$ x \in [-150^{\circ}, 210^{\circ}] $$ where $$ g(x) > f(x) $$, we need to know the function $$ f(x) $$.

Please provide the function $$ f(x) $$ so that we can analyze the graphs and find the required values of $$ x $$.

Once I have the function $$ f $$, I can assist you in determining the intervals where $$ g(x) > f(x) $$.
Cannot determine the amplitude of $$ f $$ without the function's form. To graph $$ g(x) = \cos(x - 30^{\circ}) $$ over $$ x \in [-150^{\circ}, 210^{\circ}] $$, find x-intercepts at $$ x = -60^{\circ} $$ and $$ x = 120^{\circ} $$, and y-intercept at $$ x = 0 $$ with $$ g(0) = \frac{\sqrt{3}}{2} $$. To find where $$ g(x) > f(x) $$, provide the function $$ f(x) $$ to determine the required values of $$ x $$.

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