91Ó°ÊÓ

You are given only the value \(\tan \theta\). Is it possible to find the value of \(\sec \theta\) without finding the measure of \(\theta\) ? Explain.

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.) $$ \sin (-0.65) $$

Sketch a graph of the function. $$ f(x)=\arctan 2 x $$

Use a graphing utility to graph the function. Describe the behavior of the function as \(x\) approaches zero. $$ g(x)=\frac{\sin x}{x} $$

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) \(-3.58^{\circ}\)

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.

Use a graphing utility to graph the function. Describe the behavior of the function as \(x\) approaches zero. $$ f(x)=\frac{1-\cos x}{x} $$

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.

Sketch a graph of the function. $$ f(x)=\frac{\pi}{2}+\arctan x $$

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) \(0.79^{\circ}\)