MAT-170 Precalculus Exam 3 Review

Flashcards for review of key concepts and problems from the MAT-170 Precalculus course focusing on circular motion, angles, and trigonometric functions.

What is the distance travelled by a race-car that sweeps out an angle of 3.4 radians on a track with a radius of 1.3 miles?

The distance travelled is 4.42 miles.

How do you calculate the angle swept out if the car travels 6.3 miles on a circular track with a radius of 1.3 miles?

Angle = Distance / Radius = 6.3 / 1.3 = 4.85 radians.

What function determines the vertical distance of a race-car above the center of the track in terms of the distance travelled?

Vertical distance = sin(Angle) * Radius.

How far above the center is a car when the angle swept out is 2.1 radians on a radius of 1.3 miles?

The car is 1.22 miles above the center.

What is the angle in radians corresponding to 150 degrees as Michael sweeps out on a Ferris wheel?

The angle is 2.61799 radians.

How do you convert 140 degrees to radians?

140 degrees = 140 * (π / 180) = 7π / 9 radians.

If the Ferris wheel completes 3 revolutions in 55 minutes, how many radians does it sweep out per minute?

It sweeps out 0.34 radians per minute.

Define a function f that determines Michael’s vertical distance above the ground as a function of the radian measure swept out.

f(θ) = R + R * sin(θ) where R is the radius.

What is the sine relationship for a trigonometric function that gives vertical distance above center?

The function is y = R * sin(θ) where θ is in radians.

What happens to the values of the three trigonometric functions as θ varies from 0 to π/2?

sin(θ) increases from 0 to 1, cos(θ) decreases from 1 to 0, and tan(θ) increases from 0 to ∞.

What is the measure of the angle (in radians) with vertex (0,0) and rays through points (35, 0) and (-33.807, -9.059)?

The angle is approximately 3.79 radians.

If the radius of a Ferris wheel is 35 feet, what is Michael's vertical distance after traveling 22 feet along the arc?

Michael is approximately 6.98 feet above the center.

How many feet does the angle measure (in degrees) corresponding to 2.7 km on a circular track with a radius of 4 km?

The angle swept is approximately 0.675 radians or 38.66 degrees.

Define a function g for the vertical distance of a spider above the center of a fan. If the blade is 35 meters, how is it expressed?

g(t) = 35 * sin(3t) where t is the time in seconds.

In terms of a right triangle, if sin(θ) = 0.597 and cos(θ) = 0.802, what are values for y and x?

y = 0.597, x = 0.802, and they correspond to opposite and adjacent sides respectively.

What is the period of function g if the amplitude is 2 and frequency is determined by bending a beam of 3 radians?

The period is 2π/frequency.