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Magazine Problem 3
In Exercises 1-10, find the linear speed of a point that moves with constant speed in a circular motion if the point travels along the circle of arc length \(s\) in time \(t\). Label your answer with correct units. $$ s=68,000 \mathrm{~km}, t=250 \mathrm{hr} $$
Problem 4
In Exercises 1-10, find the linear speed of a point that moves with constant speed in a circular motion if the point travels along the circle of arc length \(s\) in time \(t\). Label your answer with correct units. $$ s=7,524 \mathrm{mi}, t=12 \text { days } $$
Problem 4
In Exercises 1-10, find the measure (in radians) of a central angle \(\theta\) that intercepts an arc on a circle of radius \(r\) with indicated arc length \(s\). $$ r=6 \text { in., } s=1 \text { in. } $$
Problem 4
In Exercises 1-12, find the exact length of each arc made by the indicated central angle and radius of each circle. $$ \theta=\frac{\pi}{8}, r=6 \mathrm{yd} $$
Problem 4
In Exercises 1-14, find the exact values of the indicated trigonometric functions using the unit circle. $$ \sin \left(\frac{7 \pi}{6}\right) $$
Problem 5
In Exercises 1-10, find the linear speed of a point that moves with constant speed in a circular motion if the point travels along the circle of arc length \(s\) in time \(t\). Label your answer with correct units. $$ s=1.75 \mathrm{~nm} \text { (nanometers), } t=0.25 \mathrm{~ms} \text { (milliseconds) } $$
Problem 5
In Exercises 1-12, find the exact length of each arc made by the indicated central angle and radius of each circle. $$ \theta=\frac{2 \pi}{7}, r=3.5 \mathrm{~m} $$
Problem 5
In Exercises 1-10, find the measure (in radians) of a central angle \(\theta\) that intercepts an arc on a circle of radius \(r\) with indicated arc length \(s\). $$ r=100 \mathrm{~cm}, s=20 \mathrm{~mm} $$
Problem 5
In Exercises 1-14, find the exact values of the indicated trigonometric functions using the unit circle. $$ \sin \left(\frac{3 \pi}{4}\right) $$
Problem 6
In Exercises 1-10, find the measure (in radians) of a central angle \(\theta\) that intercepts an arc on a circle of radius \(r\) with indicated arc length \(s\). $$ r=1 \mathrm{~m}, s=2 \mathrm{~cm} $$
