Exam 3: Radian Measure

The figure is a model of George Ferris's Ferris wheel. The diameter of the wheel is 248 feet; and θ  is the central angle formed as a rider travels from his or her initial position P ₀ to position P ₁. Find the distance traveled by the rider if θ = 213° . Round your answer to the nearest tenth. s = __________ ft

A Ferris Wheel called Colossus has a diameter of 158 feet. Using the figure as a model, find the distance traveled by someone starting at initial position P ₀ and moving to position P ₁. Round your answers to the nearest tenth. if θ = 157° s = __________ feet if  θ  = 201 °  s  =  __________ feet if  θ  = 279 °  s  =  __________ feet

θ  is a central angle that cuts off an arc of length s . Find the radius of the circle if θ = 8, s = 5  ft. ​

Find the distance s covered by a point moving with linear velocity v for a time t if ​ ft/sec and sec If the answer needs rounding round it to three significant digits. __________ ft

Draw the following angle in standard position and then name the reference angle. ​

A point is traveling with uniform circular motion on a circular path of radius r . Find ω  if cm and cm/sec. If the answer needs rounding, round it to three significant digits. __________ rad/sec

Find the linear velocity of a point moving with uniform circular motion, if the point covers a distance s in an amount of time t , where ​ cm and  sec ​

For the problem below, θ  is a central angle in a circle of radius r . Find the length of arc s cut off by θ . θ = 2, r = 6  inches. If the answer needs rounding, round it to three significant digits. s = __________ inches

Use a calculator to find Please round the answer to the nearest ten-thousandth.

Use a calculator to find θ  to the nearest tenth of a degree, if and ​   with θ  in QIII ​ ​

A sector of area  in² is formed by a central angle of 45°. What is the radius of the circle? If the answer needs rounding, round it to three significant digits. r = __________ inches

Point P moves with angular velocity ω  on a circle of radius r . Find the distance s traveled by the point in time t . ​

Graph the unit circle using parametric equations with your calculator set to degree mode. Use a scale of 5. Trace the circle to find all values of t between 0° and 360° satisfying the statement. ​ __________

Find the area of the sector formed by central angle θ = 20° in a circle of radius r = 3 m. ​

Graph the unit circle using parametric equations with your calculator set to degree mode. Use a scale of 5. Trace the circle to find the sine and cosine of the angle to the nearest ten-thousandth. 265° ​ __________ ​ __________

Use a calculator to find θ  to the nearest tenth of a degree, if and ​ with θ  in QIII ​ __________°

Find θ , if  and ​ with θ  in QIV ​

Find θ , if and ​ and  θ in QIV ​ __________°

Use a calculator to find Please round the answer to the nearest ten-thousandth. ​

The earth rotates through one complete revolution every 24 hours. Since the axis of rotation is perpendicular to the equator, you can think of a person standing on the equator as standing on the edge of a disc that is rotating through one complete revolution every 24 hours. Find the angular velocity of a person standing on the equator. ​