Using a Calculator (Leaving Cert Mathematics): Revision Notes
Using a Calculator
When working with trigonometry, your scientific calculator is an essential tool for finding trigonometric ratios and angles accurately. Understanding how to use the calculator keys properly will help you solve problems efficiently and get the correct answers.
A scientific calculator is indispensable for trigonometry problems. While you can solve some basic problems manually, real-world angles and calculations almost always require calculator precision for accurate results.
Basic trigonometric keys
Your calculator has three main trigonometric function keys that you'll use regularly:
- sin key for finding sine ratios
- cos key for finding cosine ratios
- tan key for finding tangent ratios
To find the sine, cosine, or tangent of any angle, simply press the appropriate key followed by the angle value and equals.
Finding sin 35°:
Step 1: Press the sin key
Step 2: Enter 35
Step 3: Press =
Step 4: The result will be 0.573576... = 0.5736 (to 4 decimal places)
Working with degrees and minutes
Sometimes angles are given in degrees and minutes rather than decimal degrees. Understanding this notation is crucial for accurate calculations.
Key definition: A degree can be divided into 60 parts, and each part is called 1 minute, written as 1'.
Therefore: 1° = 60'
Converting between formats
When you encounter an angle like 34°30', you have two methods to enter this into your calculator:
Method 1: Convert to decimal degrees first
- 34°30' = 34.5°
- Then press: tan 34.5 =
- Result = 0.6873
Method 2: Use the degrees/minutes key
- Press: tan 34 °/'" 30 °/'" =
- Result = 0.6873
Both methods give the same result, so choose whichever you find easier to use. The °/'" key is particularly useful for complex angle measurements, but converting to decimal degrees first can sometimes be more straightforward for mental calculations.
Inverse trigonometric functions
When you know a trigonometric ratio and need to find the angle, you use the inverse trigonometric functions:
- sin⁻¹ (inverse sine)
- cos⁻¹ (inverse cosine)
- tan⁻¹ (inverse tangent)
To access these inverse functions, you need to use the SHIFT key on your calculator. This is a critical step that students often forget - without SHIFT, you'll get the ratio instead of the angle!
How to find angles from ratios
If you're given that sin A = 0.8661, you can find angle A by following this process:
- Press SHIFT then sin (this gives you sin⁻¹)
- Enter 0.8661
- Press =
- The result is 60.008° = 60° (to the nearest degree)
The same process works for cosine and tangent:
- For tan B = 1.2734: Press SHIFT tan 1.2734 =
- Result is 51.86° (correct to 2 decimal places)
Worked example: Step-by-step calculator usage
Comprehensive Calculator Example
Let's work through a comprehensive example that shows both types of calculations:
Part (i): Find cos 72°18', correct to 4 decimal places
Step 1: Recognise this uses degrees and minutes notation
Step 2: Press cos 72 °/'" 18 °/'" =
Step 3: The result is 0.3040
Alternative method: Convert 18' to decimal degrees first:
- 18' = 18/60 = 0.3°
- So 72°18' = 72.3°
- Then press cos 72.3 =
Part (ii): If sin A = 0.5216, find A correct to the nearest degree
Step 1: Use the inverse sine function
Step 2: Press SHIFT sin 0.5216 =
Step 3: The result is 31.44°
Step 4: Round to the nearest degree: A = 31°
Calculator tips for exams
Essential Calculator Tips for Success:
- Always check your calculator is in degree mode - most trigonometry problems use degrees, not radians
- Round only your final answer - keep full precision during calculations
- Double-check the °/'" key usage - it may need to be pressed twice for degrees and minutes
- Use brackets when working with fractions in trigonometric calculations
- Practice the SHIFT key combinations - knowing these quickly will save time in exams
Common calculation scenarios
You'll typically encounter three main types of problems:
- Finding a ratio from an angle: Use sin, cos, or tan keys directly
- Finding an angle from a ratio: Use SHIFT with sin, cos, or tan keys
- Working with degrees and minutes: Use the °/'" key or convert to decimal degrees
Each type requires a different approach, but the calculator processes remain consistent once you understand the key sequences.
Key Points to Remember:
- Use sin, cos, and tan keys to find trigonometric ratios from angles
- Use SHIFT with trigonometric keys to find angles from ratios (inverse functions)
- 1° = 60' - degrees can be divided into 60 minutes
- The °/'" key helps you enter degrees and minutes directly into your calculator
- Always check your calculator is in degree mode for trigonometry problems