4. consider the function f(x)=cos 6x. 4a determine the period of the function in degrees. period = 60…

Explanation:

Step1: Recall cosine - function period formula

For the function $y = A\cos(Bx + C)+D$, the period $T$ in degrees is given by $T=\frac{360^{\circ}}{|B|}$. Here $B = 6$, so $T=\frac{360^{\circ}}{6}=60^{\circ}$.

Step2: Calculate number of cycles

To find the number of cycles in an angle $\theta$, we use the formula $n=\frac{\theta}{T}$. Given $\theta = 3240^{\circ}$ and $T = 60^{\circ}$, then $n=\frac{3240^{\circ}}{60^{\circ}}=54$.

Step3: Determine maximum value

The general form of the cosine function is $y=\cos(x)$ and its range is $[- 1,1]$. For $y = \cos(6x)$, the maximum value of the cosine - function is 1.

Step4: Determine minimum value

The range of the cosine function $y=\cos(x)$ is $[-1,1]$. For $y=\cos(6x)$, the minimum value of the cosine - function is - 1.

Answer:

4a. $60$ degrees 4b. $54$ 4c. $1$ 4d. $-1$