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Chapter 4: Problem 32

Use a calculator to evaluate each function. Round your answers to four decimal places. (Be sure the calculator is in the correct mode.) (a) \(\tan 23.5^{\circ}\) (b) \(\cot 66.5^{\circ}\)

Short Answer

Expert verified
The result is not provided due to the nature of the problem. Each student must calculate and round it on their own calculator.

Step by step solution

01

Set Calculator to Degree Mode

Firstly, ensure that your calculator is set to degree mode. This setting is crucial because the values provided in the exercise are in degrees rather than radians. The method for switching modes depends on your calculator model, but usually, you'll find this option in the settings or mode menu.
02

Evaluate Tangent Function

Enter '23.5' into your calculator, then press the 'tan' button to calculate the tangent of 23.5 degrees. The value that appears on your calculator represents \(\tan 23.5^{\circ}\).
03

Round the Answer for Part (a)

The calculator's result will likely go on for many decimal places. You need to round this number to four decimal places, as the exercise instructs. Once you've done this rounding, you have the answer to part (a).
04

Evaluate Cotangent Function

To calculate cotangent, you need to take the reciprocal of the tangent value. Most calculators don't have a cotangent button, so you enter '66.5', press the 'tan' button, then take the reciprocal (1 梅 answer) to find \(\cot 66.5^{\circ}\).
05

Round the Answer for Part (b)

Again, the answer on your calculator will likely be a long decimal. Round this to the nearest four decimal places to find your answer to part (b).

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Most popular questions from this chapter

Use a graphing utility to graph the functions \(f(x)=\sqrt{x}\) and \(g(x)=6\) arctan \(x .\) For \(x>0,\) it appears that \(g>f .\) Explain why you know that there exists a positive real number \(a\) such that \(ga .\) Approximate the number \(a\).

Define the inverse cotangent function by restricting the domain of the cotangent function to the interval \((0, \pi),\) and sketch the graph of the inverse trigonometric function.

Sketch a graph of the function. $$g(t)=\arccos (t+2)$$

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. $$g(x)=\frac{\sin x}{x}$$

Determine whether the statement is true or false. Justify your answer. $$\sin \frac{5 \pi}{6}=\frac{1}{2} \quad \rightarrow \quad \arcsin \frac{1}{2}=\frac{5 \pi}{6}$$
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