## Trigonometric Function Values in Tables

As you work through this chapter, you will learn about different applications of the trig functions. In many cases, you will need to find the value of a function of an angle that is not necessarily one of the "special" angles we have worked with so far. Traditionally, textbooks have provided students with tables that contain values of the trig functions. Below is a table that provides approximate values of the sine, cosine, and tangent values of several angles.

Angle | Cosine | Sine | Tangent |

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We can use the table to identify approximate values.

**Example 6:** Find the approximate value of each expression, using the table above.

a.

b.

c.

**Solution:**

a.

We can identify the sine value by finding the row in the table for . The sine value is found in the third row of the table. Note that this is an approximate value. We can evaluate the reasonableness of this value by thinking about an angle that is close to , . We know that the ordered pair for is , so the sine value is , which is also in the table. It is reasonable that which is slightly less than the sine value of , given where the terminal sides of these angles intersect the unit circle.

b.

We can identify this cosine value by finding the row for . The cosine value is found in the second column. Again, we can determine if this value is reasonable by considering a nearby angle. is between and , and its cosine value is between the cosine values of these two angles.

c.

We can identify this tangent value by finding the row for , and reading the final column of the table. In the review questions, you will be asked to explain why the tangent value seems reasonable.

## Using a Calculator to Find Values

**Video: Determining trig function values on the calculator**

If you have a scientific calculator, you can determine the value of any trig function for any angle. Here we will focus on using a TI graphing calculator to find values.

First, your calculator needs to be in the correct "mode." In chapter 2 you will learn about a different system for measuring angles, known as radian measure. In this chapter, we are measuring angles in degrees. (This is analogous to measuring distance in miles or in kilometers. It's just a different system of measurement.) We need to make sure that the calculator is working in degrees. To do this, press **[MODE]**. You will see that the third row says Radian Degree. If Degree is highlighted, you are in the correct mode. If Radian is highlighted, scroll down to this row, scroll over to Degree, and press **[ENTER]**. This will highlight Degree. Then press **[Mode]** to return to the main screen.

Now you can calculate any value. For example, we can verify the values from the table above. To find , press **[SIN][130][ENTER]**. The calculator should return the value .

You may have noticed that the calculator provides a "(" after the SIN. In the previous calculation, you can actually leave off the ")". However, in more complicated calculations, leaving off the closing ")" can create problems. It is a good idea to get in the habit of closing parentheses.

You can also use a calculator to find values of more complicated expressions.

**Example 7:** Use a calculator to find an approximate value of . Round your answer to places.

**Solution:**

To use a TI graphing calculator, press **[SIN][25][+][COS][25][ENTER]**. The calculator should return the number . This rounds to

**How does the calculator determine trig function values?**

Related articles

http://www.homeschoolmath.net/teaching/sine_calculator.php http://en.wikipedia.org/wiki/Exact_trigonometric_constants