91Ó°ÊÓ

Use a calculator to evaluate the trigonometric function. Round your answer to four decimal places. (Be sure the calculator is set in the correct angle mode.) $$ \text { sec } 225^{\circ} $$

Use a graphing utility to graph the function and the damping factor of the function in the same viewing window. Describe the behavior of the function as \(x\) increases without bound. $$ f(x)=2^{-x / 4} \cos \pi x $$

Convert each angle measure to decimal degree form without using a calculator. Then check your answers using a calculator. (a) \(-135^{\circ} 36^{\prime \prime}\) (b) \(-408^{\circ} 16^{\prime} 20^{\prime \prime}\)

Convert each angle measure to degrees, minutes, and seconds without using a calculator. Then check your answers using a calculator. $$ \text { (a) } 240.6^{\circ} $$

Convert each angle measure to degrees, minutes, and seconds without using a calculator. Then check your answers using a calculator. (a) \(-345.12^{\circ}\) (b) \(0.45^{\circ}\)

For a person at rest, the velocity \(v\) (in liters per second) of airflow during a respiratory cycle (the time from the beginning of one breath to the beginning of the next) is given by \(v=0.85 \sin \frac{\pi t}{3},\) where \(t\) is the time (in seconds). (Inhalation occurs when \(v>0,\) and exhalation occurs when \(v<0 .\) ) (a) Find the time for one full respiratory cycle. (b) Find the number of cycles per minute. (c) Sketch the graph of the velocity function.

Convert each angle measure to degrees, minutes, and seconds without using a calculator. Then check your answers using a calculator. (a) \(2.5^{\circ}\) (b) \(-3.58^{\circ}\)

Convert each angle measure to degrees, minutes, and seconds without using a calculator. Then check your answers using a calculator. (a) \(-0.36^{\circ}\) (b) \(0.79^{\circ}\)

After exercising for a few minutes, a person has a respiratory cycle for which the velocity of airflow is approximated by \(v=1.75 \sin \frac{\pi t}{2},\) where \(t\) is the time (in seconds). (Inhalation occurs when \(v>0,\) and exhalation occurs when \(v<0 .\) ) (a) Find the time for one full respiratory cycle. (b) Find the number of cycles per minute. (c) Sketch the graph of the velocity function.

The daily consumption \(C\) (in gallons) of diesel fuel on a farm is modeled by $$C=30.3+21.6 \sin \left(\frac{2 \pi t}{365}+10.9\right)$$ where \(t\) is the time (in days), with \(t=1\) corresponding to January 1 . (a) What is the period of the model? Is it what you expected? Explain. (b) What is the average daily fuel consumption? Which term of the model did you use? Explain. (c) Use a graphing utility to graph the model. Use the graph to approximate the time of the year when consumption exceeds 40 gallons per day.