Chapter 4.2, Problem 73E

(a)

To determine

To calculate: The value of t using the given figure and a straightedge and then to check the approximation using a graphing utility.

Answer to Problem 73E

  $t\approx 0.25or2.89$ .

Explanation of Solution

Given information: A figure is provided.

Calculation: Assume that any point on the provided circle of unit length be denoted by where

• Here, is the arc length or the angle measured in radians and 3’o clock from the standard position.

Here,

The point that can be pointed on the circle is approximately,

  $(\cos t,\sin t)=(x,0.25)$

The corresponding value of t in radians is 0.25 or $2.89$ .

The graph has shown using a graphing utility as follows:

  

The value can be approximated (in radians) using a calculator as,

  $\begin{array}{l}\sin 0.25=0.24740395925\\ \approx 0.25\\ and\\ \sin 2.89=0.24894678667\\ \approx 0.25\end{array}$

Hence, $t\approx 0.25or2.89$ .

(b)

To determine

To calculate: The value of t using the given figure and a straightedge and then to check the approximation using a graphing utility.

Answer to Problem 73E

  $t\approx 1.82or4.46$ .

Explanation of Solution

Given information: A figure is provided.

Calculation:

Assume that any point on the provided circle of unit length be denoted by where

• Here, is the arc length or the angle measured in radians and 3’o clock from the standard position.

Here, $\cos t=-0.25$ .

The point that can be pointed on the circle is approximately,

  $(\cos t,\sin t)=(-0.25,y)$

The corresponding value of t in radians is $1.82or4.46$ .

The graph has shown using a graphing utility as follows:

  

The value can be approximated (in radians) using a calculator as,

  $\begin{array}{l}\cos 1.82=-0.24663230996\\ \approx -0.25\\ and\\ \cos 4.46=-0.24971796382\\ \approx -0.25\end{array}$

Hence, $t\approx 1.82or4.46$ .