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Chapter 6: Problem 85

Find the function value. Round to four decimal places. $$\tan 310.8^{\circ}$$

Short Answer

Expert verified
0.4843

Step by step solution

01

Convert to radians if needed

First, it is important to note that the value 310.8 degrees can directly be used in trigonometric calculations, so no conversion to radians is necessary for this problem.
02

Use the tan function on your calculator

Enter the value 310.8 into your calculator and use the tan function to find the tangent of 310.8 degrees. Make sure the calculator is set to degrees and not radians.
03

Round to four decimal places

The calculator should give you a value. This value needs to be rounded to four decimal places for the final answer.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

tangent function
The tangent function, often written as \tan\theta, is one of the primary trigonometric functions. It relates the angles of a triangle to the ratios of its sides. Specifically, the tangent of an angle in a right triangle is the ratio of the length of the opposite side to the length of the adjacent side. To find \(\tan\theta\), you can use the formula \(\tan\theta = \frac{\text{opposite}}{\text{adjacent}}\). The tangent function is periodic, with a period of 180 degrees (or \pi radians), and it is undefined at \(\theta = 90^\text{\degree}\) plus all multiples of 180 degrees.
degree measure
Degrees are a unit of measurement for angles, commonly used in trigonometry. One complete revolution is divided into 360 equal parts, known as degrees. In the context of calculating \(\tan 310.8^\text{\degree}\), 310.8 degrees is simply an angle that can be input directly into a calculator set to degree mode. It鈥檚 important to set your calculator properly to degrees before performing any calculations involving angles measured in degrees. Always check if the problem specifies using degrees or radians to avoid errors.
calculator usage
Using a calculator for trigonometric functions involves a few crucial steps to ensure accuracy. First, ensure your calculator is set to degrees, not radians. On most calculators, this can be done by selecting the DEG mode. Next, input the angle value (in this case, 310.8) and press the TAN button to compute the tangent value. Calculators can vary slightly, so refer to your calculator's manual if you have trouble finding settings or functions. After getting the value, you'll need to convert it into a required format, like rounding to four decimal places.
rounding numbers
Rounding numbers is an essential math skill, especially when you need specific precision, like in trigonometry problems. When the problem requires rounding to four decimal places, follow these steps: check the fifth decimal place. If this digit is 5 or greater, you round up the fourth decimal place by one. If it's less than 5, you leave the fourth decimal place as it is. For example, if your calculator gives a tangent value of 1.234567, you will round it to 1.2346. This ensures the result is accurate to the requested precision.

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Most popular questions from this chapter

Find the reference angle and the exact function value if they exist. $$\sin \left(-135^{\circ}\right)$$

Find the reference angle and the exact function value if they exist. $$\cos 90^{\circ}$$

Use a calculator in Exercises \(81-84,\) but do not use the trigonometric function keys. Given that \(\sin 41^{\circ}=0.6561\) \(\cos 41^{\circ}=0.7547\) \(\tan 41^{\circ}=0.8693\) find the trigonometric function values for \(319^{\circ} .\)

Classify the function as linear, quadratic, cubic, quartic, rational, exponential, logarithmic, or trigonometric. $$f(x)=\frac{x+4}{x}[4.5]$$

The transformation techniques that we learned in this section for graphing the sine and cosine functions can also be applied to the other trigonometric functions. Sketch a graph of each of the following. Then check your work using a graphing calculator. $$y=2 \tan \left(\frac{1}{2} x\right)$$
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