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Chapter 4: Problem 66

Use a calculator to find the value of the trigonometric function to four decimal places. $$\sec 1$$

Short Answer

Expert verified
Without knowing the unit used for 1 (degree or radians), we cannot accurately give a numeric answer. However, for the procedure from step 1 to step 3, the result will be the four decimal point value of \(\sec 1\) for the unit used.

Step by step solution

01

Transform Sec into Cosine

Transform the \(\sec 1\) into \(1/\cos 1\). This converts the problem into a form that can be done directly using the calculator. Even if the calculator does not have the secant function, it surely will have the cosine function.
02

Calculate \(\cos 1\)

Use the calculator to find the value of \(\cos 1\). Make sure that the calculator is set to the correct mode (degrees or radians) based on the given values.
03

Calculate \(1/\cos 1\)

Divide 1 by the result obtained in step 2. This will give the value of \(\sec 1\).

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Most popular questions from this chapter

In Chapter \(5,\) we will prove the following identities: $$ \begin{aligned} \sin ^{2} x &=\frac{1}{2}-\frac{1}{2} \cos 2 x \\ \cos ^{2} x &=\frac{1}{2}+\frac{1}{2} \cos 2 x \end{aligned} $$ Use these identities to solve. Use the identity for \(\sin ^{2} x\) to graph one period of \(y=\sin ^{2} x\)

The number of hours of daylight in Boston is given by $$ y=3 \sin \frac{2 \pi}{365}(x-79)+12 $$ where \(x\) is the number of days after January 1 a. What is the amplitude of this function? b. What is the period of this function? c. How many hours of daylight are there on the longest day of the year? d. How many hours of daylight are there on the shortest day of the year? e. Graph the function for one period, starting on January 1

Use a graphing utility to graph each function. Use a viewing rectangle that shows the graph for at least two periods. $$y=\cot 2 x$$

Determine whether each statement makes sense or does not make sense, and explain your reasoning. After using the four-step procedure to graph \(y=-\cot \left(x+\frac{\pi}{4}\right),\) I checked my graph by verifying it was the graph of \(y=\cot x\) shifted left \(\frac{\pi}{4}\) unit and reflected about the \(x\) -axis.

Determine whether each statement makes sense or does not make sense, and explain your reasoning. If \(\theta=\frac{3}{2},\) is this angle larger or smaller than a right angle?
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