MAT1793-ABED_1: Important Calculator Instructions

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Until now, you have been referencing the tangent table to determine an angle measure from a tangent ratio or the tangent ratio from an angle measure. The table you've been using provides the approximated ratios for some angle measures, but not all. Fortunately, most scientific and most graphing calculators are able to provide this information for all angle measures.

To determine the tangent ratio of an angle, use the "tan" function on your calculator.

Testing Your Calculator: Angle Measure to Ratio

Determine the value of tan 42.7°

Use the tan function on your calculator.

For some calculators you will enter: tan 42.7 enter or = .

For some calculators you will enter: 42.7 tan = .

If you have entered it correctly into your calculator, you should get an answer of 0.92277...

tan 42.7° = 0.92277...

It may help to think of this tan 42.7° value as part of the table from earlier in the lesson.

θ	\(\frac{\text{length opposite}\,\theta}{\text{length adjacent to}\,\theta}\)	tan θ
35°	0.70	0.70
40°	0.84	0.84
42.7°	0.92277...	0.92277...
45°	1	1
50°	1.19	1.19

All angles in this course are measured in degrees, so you will need to make sure your calculator is in degree mode. Many calculators show a "D" or "deg" when in degree mode.
- Try to determine the value of tan 42.7°. If you get an answer of 0.92277..., you are in the correct mode.
- If you get an answer of -3.369... or 0.796..., you are in the wrong mode. If you receive any other value, you may be entering the information incorrectly.
If you are unsure how to change the mode of your calculator, refer to your calculator's manual, or contact your teacher.

Testing Your Calculator: Ratio to Angle Measure

To determine the angle measures from a tangent ratio, use the "tan^-1" function. Some calculators label this function "arctan".

Determine an angle measure with a tangent ratio of 0.5

Use the tan^-1 function on your calculator.

For some calculators you will enter: tan^-1 0.5 enter or = .

For some calculators you will enter: 0.5 tan^-1 = .

If you have entered it correctly into your calculator, you should get an answer of 26.56505...

tan^-1 (0.5) = 26.56505...°

Again, it may help to think of this value as part of the table from earlier in the lesson.

θ	\(\frac{\text{length opposite}\,\theta}{\text{length adjacent to}\,\theta}\)	tan θ
20°	0.36	0.36
25°	0.47	0.47
26.565...°	0.50	0.50
30°	0.58	0.58
35°	0.70	0.70

It is essential that you learn how to use the trigonometric functions on your calculator. If you were not able to obtain the previous two values using your calculator, contact your teacher for assistance.

Trigonometric ratios produced from an angle are often long decimals. To ensure accurate answers, wait to evaluate the tangent ratio until the last step of a calculation, where possible.