Question

The equation r = 4sin(θ) represents a circle. What is the radius of the circle, and what is the symmetry of the graph? The radius is 2 units, and the graph is symmetric about the line Theta = StartFraction pi Over 2 EndFraction. The radius is 4 units, and the graph is symmetric about the line Theta = StartFraction pi Over 2 EndFraction. The radius is 2 units, and the graph is symmetric about the polar axis. The radius is 4 units, and the graph is symmetric about the polar axis.

Answer 1

Answer:

1) 270 degrees

2)  pi/4 rad

Step-by-step explanation:

1.) For which value of theta is sine theta = negative 1?

Given

sintheta = -1

theta = arcsin(-1)

theta = -90degrees

Since sin is negative in the third and 4th quadrant

In the third quadrant, theta = 180 + 90 = 270degrees

In the fourth quadrant, theta = 360 - 90 = 270 degrees

Hence the required value of theta is 270degrees

2) Given the radius of the circle to be 1, the y axis value will also be 1 units

Opposite = 1

adjacent = 1

hyp = √1²+1²

hyp = √2

sin theta = opp/hyp

sin theta = 1/√2

theta = arccsin(1/√2)

theta = 45 degrees

Express in radians

45 degrees = pi/4 radians

Hence the required angle in the first quadrant is pi/4 rad

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