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### 16.4. Evaluating a Trigonometric Expression

Before we solve trigonometric equations in the following section, let us first evaluate some trigonometric expressions. By that we mean to find the numerical value of the expression. We will do that by calculator.

Simply perform the indicated operations. Just remember that angles are assumed to be in radians unless marked otherwise. The following examples show the calculations with intermediate steps written down; for comparison, the screens show the work done in a single step. Use the method with which you feel most comfortable.

## Example 22:

Evaluate the following to three significant digits:

7.82 − 3.15 cos 67.8°

Solution: By calculator, we find that cos 67.8° = 0.3778, so our expression becomes

7.82 − 3.15(0.3778) = 6.63

As usual when doing such calculations, we keep all the figures in the calculator whenever possible. If you must write down an intermediate result, as we did here just to show the steps, retain 1 or 2 digits more than required in the final answer.

TI-83/84 screen for Example 22. The calculator was in DEGREE mode for this example.

TI-83/84 screen for Example 23, done in a single step. Here the calculator was in RADIAN mode.

## Example 23:

Evaluate the following to four significant digits:

1.836 sin 2 + 2.624 tan 3

Solution: ...

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