Problem 75
Question
Express each angular speed in radians per second. 6 revolutions per second
Step-by-Step Solution
Verified Answer
The angular speed is \(12\pi\) radians per second.
1Step 1: Identify the conversion factor
One revolution is equal to \(2\pi\) radians. This is the conversion factor that will be used.
2Step 2: Set up the conversion
The given angular speed is 6 revolutions per second. Write this as \(6 \, \text{revolutions/second}\). To convert this to radians per second, multiply by the conversion factor:\(6 \, \text{revolutions/second} \times 2\pi \, \text{radians/revolution}\). We can cancel out the 'revolution' units, leaving us with radians/second.
3Step 3: Perform the multiplication
Perform the multiplication to get the final result. \(6 \times 2\pi = 12\pi\).
Other exercises in this chapter
Problem 74
Let $$ \sin t=a, \cos t=b, \text { and } \tan t=c $$ Write each expression in terms of \(a, b,\) and \(c\). $$3 \cos (-t)-\cos t$$
View solution Problem 75
Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. $$\tan ^{2} 15^{\circ}-\
View solution Problem 75
In Exercises \(61-86,\) use reference angles to find the exact value of each expression. Do not use a calculator. $$\tan \left(-\frac{\pi}{4}\right)$$
View solution Problem 75
Let $$ \sin t=a, \cos t=b, \text { and } \tan t=c $$ Write each expression in terms of \(a, b,\) and \(c\). $$\sin (t+2 \pi)-\cos (t+4 \pi)+\tan (t+\pi)$$
View solution