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## Problem 1 Solution

```0.93541

```

### Solution Steps for Problem 1

The key: Convert the words into an expression that you can evaluate with your calculator. How you solve the problem at this point depends upon how confident you are in using your calculator. Try solving it both ways as suggested below so you are convinced that your scientific calculator works in a way you really do understand!

### Method: Straight-forward entry into Scientific Calculator:

1. Note first that it does not matter for this problem whether we are in degrees mode or radians, since we will be taking the sine of an angle which will be given by the inverse tangent function. Also, remember that the key TAN-1 does not mean "one over tangent" but "the angle whose tangent is."

2. Think of this as a "nested" problem: you want to calculate the sine of an angle, and the angle is the angle whose tangent is the square root of 7. Use the following key strokes:
` SIN   TAN-1  SQRT  7   ENTER `

### Method: Stepwise Calculation of Each Piece:

1. We need the square root of 7. Intermediate answer: 2.64575
2. We need to find the angle whose tangent is this number: Intermediate answer: 1.20943 radians
3. We need to find the sine of this angle: 0.93541
In this latter example, you may have to use your ANS key to get the previous answer entered in the right order. On a TI-82 type calculator, this second way of stepping through the calculations takes many more key strokes than the first, so if you do not need the intermediate answers, the first method is preferred.

Next Try It Out Problem.

Developed by
Shodor
in cooperation with the Department of Chemistry,
The University of North Carolina at Chapel Hill