Question

Lab м м 281) Groph ye 1+2 cos (4x). Show a.) Cosine curre b.) dasked midlice c.) X-values of Start and end it. & full cycle.

Answer 1

Solution:

General equation of cosine equation:

y = Acos(B(x - C) + D

where A is amplitude,

C is phase shift,

D is midline,

$\small 2\pi /B$ is period of funtion.

$\small y = 1+2cos\left ( \frac{x}{4} \right )$

Amplitude(A) = 2

Phase shift(C) = 0

Midline(D) = 1

B = 1/4

$\small \textup{Period =}\frac{2\pi }{B}=\frac{2\pi }{1/4}=8\pi$

Start point:

At x = 0,

$\small y = 1+2cos\left ( 0 \right )=1+2=3$

End point:

Since Period is $\small 8\pi$ ,

End point of one cycle is $\small x=8\pi$ ,

$\small y = 1+2cos\left ( 2\pi \right )=1+2=3$

-27 т 2.g 2 о h — 19; д midline 2+ (5)я 5ozz+1= 2. (28) (g'a