Question

Convert 6∘ to radians, correct to 4 decimal places. 6∘= ____________ rad (4 dec. places). Convert 4.75 rad to degrees, correct to 4 decimal places. 4.75 rad = ____________ degrees (4 dec. places).

Question b: (2 points) Determine the length of an arc of a circle with radius 6 metres that subtends a central angle of 300∘ to two decimal places. Arc length, s= ____________ m. c A circular wheel of radius 0.55 metres is spinning at a rate of 135 revolutions per minute. What are the angular speed (in rad/s) and the linear speed (in m/s) of a point on the circumference of the wheel to 2 decimal places? Angular speed, ω= ____________ rad/s (2 dec. places). Linear speed, v= ____________ m/s (2 dec. places) Determine the area of the corresponding sector of the circle with radius 6 and central angle 300∘ to two decimal places. Area of sector, A= ____________ m2.

Answer 1

Convert 6∘ to radians, correct to 4 decimal places.

To convert from degree to radians, multiply the degree measure by π/180°

6° * π/180° = 0.1047 radians

6° = 0.1047 rad

Convert 4.75 rad to degrees, correct to 4 decimal places.

To convert from radians to degrees, multiply the radian measure by 180°/π

4.75 rad * 180°/π = 272.1550°

4.75 rad = 272.1550°

Determine the length of an arc of a circle with radius 6 metres that subtends a central angle of 300° to two decimal places.

Length of arc, s = rθ

r : radius of the circle

θ : angle in radians

300° = 300° * π/180° = 5π/3 rad

s = 6 * 5π/3 = 31.42 metres

Arc length = 31.42 metres

A circular wheel of radius 0.55 metres is spinning at a rate of 135 revolutions per minute. What are the angular speed (in rad/s) and the linear speed (in m/s) of a point on the circumference of the wheel to 2 decimal places?

135 revolutions per minute = 135 * 2π radians per minute = 270π radians per minute

270π radians per minute = 270π/60 radians per second = 4.5π radians per second = 14.14 rad/s

Angular speed : 14.14 rad/s

1 revolution = 2πr metres

135 revolutions per minute = 135 * 2π * 0.55 metres per minute

135 * 2π * 0.55 metres per minute = 148.5π/60 metres per second = 7.78 m/s

Linear speed : 7.78 m/s

Determine the area of the corresponding sector of the circle with radius 6 and central angle 300° to two decimal places.

Area of sector, A = 1/2 * r^2θ

r : radius of the circle

θ : angle in radians

A = 1/2 * 6^2 * 5π/3 = 94.25 m^2

Area of sector = 94.25 m^2