Exploring Arc Length and Sector Area in Trigonometry

What formula is used to calculate the area of a circle?

• Area = pi * d

• Area = 2 * pi * r

• Area = pi * r^2

• Area = r^2 / 2

How is the arc length of a circle sector determined?

• Arc length = Circumference * (Central angle / 360)

• Arc length = Area * (Central angle / 360)

• Arc length = Circumference * (Central angle / 2 * pi)

• Arc length = Circumference * (Central angle / Full circle angle)

How is the sector area of a circle calculated?

• Sector area = (Central angle / Full circle angle) * Circumference

• Sector area = (Central angle / Full circle angle) * Area

• Sector area = (Central angle / 2 * pi) * pi * r^2

• Sector area = (Central angle / 360) * pi * r^2

What is the grazing area available to Zoe the goat?

• 450 Pi square meters

• 900 Pi square meters

• 700 Pi square meters

• 550 Pi square meters

What is the reference angle for an angle of -7 pi / 6?

• pi / 6

• 5 pi / 6

• -pi / 6

• 7 pi / 6

What is the reference angle for an angle of 17 pi / 12?

• 12 pi / 17

• 7 pi / 12

• 5 pi / 12

• pi / 12

What is the equation of a circle with a radius of 4 units?

• x^2 + y^2 = 16

• x^2 + y^2 = 8

• x^2 + y^2 = 4

• x^2 + y^2 = 12

What trigonometric function represents the ratio of the opposite side to the hypotenuse?

• Sine

• Cosine

• Tangent

• Secant

How do you calculate the cosine of an angle in a right triangle?

• Cosine = Adjacent / Hypotenuse

• Cosine = Opposite / Hypotenuse

• Cosine = Opposite / Adjacent

• Cosine = Hypotenuse / Adjacent

If a point on the terminal side of theta is (-4,3), what is the cosine of theta?

• 4 / 3

• -3 / 4

• 3 / 5

• -4 / 5