Chapter 4.2, Problem 72E

(a)

To determine

To calculate: The value of $\sin 0.75$ using the given figure and a straightedge and then to check the approximation using a graphing utility.

Answer to Problem 72E

The value of $\sin 0.75$ is approximately equal to 0.7

Explanation of Solution

Given information: A figure is provided.

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

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

Now, to calculate $\sin 0.75$ , observe that

The point that can be pointed on the circle is approximately equal to

Therefore,

  

The graph using a graphing utility as follows:

  

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

  

Hence, $\sin 0.75\approx 0.7$ .

(b)

To determine

To calculate: The value of $\cos 2.5$ using the given figure and a straightedge and then to check the approximation using a graphing utility.

Answer to Problem 72E

The value of $\cos 2.5$ is approximately equal to $-0.8$ .

Explanation of Solution

Given information: A figure is provided.

Calculation:

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

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

Now, to calculate $\cos 2.5$ , observe that $\theta =2.5$ .

The point that can be pointed on the circle is approximately equal to $(-0.8,0.6)$ .

Therefore,

  $\begin{array}{l}\cos 2.5=x\\ =-0.8\end{array}$

The graph using a graphing utility as follows:

  

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

  $\begin{array}{l}\cos 2.5=-0.80114361554\\ \approx -0.8\end{array}$

Hence, $\cos 2.5\approx -0.8$.