Question

11:43 AM Sun May 12 X Jocelyn Rodriguezmoya P3.3 graph polar assignment.pdf Date: Period: Pre-Cal/ WEED Name: Assignment P3.3 polar Graph each equation without using a calculator and name the type of graph. 1. r-3cos30 2. r 3sin2 . rcose-4

Answer 1

1.

r = 3cos(39)

The number multiplied to cos(3$\theta$) is 3.

Hence, the amplitude should be [3,-3] instead of [1,-1]

Now,
cos(30)
, the 3 multiplied to $\theta$ shows that the time period should be 1/3 of the original time period

Or the time period should become 2$\pi$/3

The behaviour would remain the same as that of Cos with changes in amplitude and time period.

Hence, drawing the graph we would get

f (x) 3cos (3x) -2

The graph is sinusoidal.

2.

3sin(29) r

The number multiplied to sin(2$\theta$) is 3.

Hence, the amplitude should be [3,-3] instead of [1,-1]

Now,
sin(20)
, the 2 multiplied to $\theta$ shows that the time period should be 1/2 of the original time period

Or the time period should become $\pi$

The behaviour would remain the same as that of Sin with changes in amplitude and time period.

Hence, drawing the graph we would get

f (x) 3sin (2x)

The graph would be sinusoidal

3.

r = 4cos(49)

The number multiplied to cos(4$\theta$) is 4.

Hence, the amplitude should be [4,-4] instead of [1,-1]

Now,
cos(40)
, the 4 multiplied to $\theta$ shows that the time period should be 1/4 of the original time period

Or the time period should become $\pi$/2

The behaviour would remain the same as that of Cos with changes in amplitude and time period.

Hence, drawing the graph we would get

f (x)-4cos (4x)

The graph is sinusoidal

4.

r²=9sin2$\theta$

$r=\pm 3\sqrt{sin2\theta}$

Amplitude will be 3.

The positive and negative will be a mirror of each other.

The domain of $\theta$ would be [0,$\pi$/2] as above it would become a negative inside root.

The period would be $\pi$.

Hence, drawing the graph, we would get

2 -8 -6 -4 -2 0 2 6 8 -10

The graph is periodic and discontinuous

5)

$rcos\theta = 4$

$r= 4sec\theta$

The graph would a normal sec graph with the lowest point being 4 and -4 i.e., r can obtain all real values except [4,-4]

The time period is 2$\pi$.

The graph would be

10 15 10 15

The graph is periodic, discontinuous and non-sinusoidal.

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