S3 Mathematics - Term 1

Topic 1: Trigonometry I

Lesson 4: Using Calculators for Trig Values

Duration: 40 minutes

Learning Outcomes

By the end of this lesson, you should be able to:

• Use a scientific calculator to find sine, cosine, tangent values
• Ensure calculator is in degree mode
• Find trig ratios for any angle from 0 to 90 degrees

The Problem

Question: What is sin 37 degrees?

Without calculator:

• Draw perfect triangle with 37 degrees angle
• Measure sides very carefully
• Calculate the ratio
• Very difficult and time-consuming!

The Solution

Calculators!

• Mathematicians have calculated these values
• Stored in calculator memory
• Get any trig value instantly
• Essential practical skill!

Calculator Trig Buttons

Find these on your calculator:

• sin button (often red or blue)
• cos button
• tan button

Usually in the top rows

CRITICAL: Degree Mode

Calculators have two angle modes:

• DEG (degrees) ← We use this!
• RAD (radians) ← Advanced math only

Check your screen shows "DEG"

Setting Degree Mode

1. Press MODE or SETUP button
2. Find angle setting
3. Select DEG (degrees)
4. Screen should show "DEG" or "D"

Ask if you need help!

Finding sin 30 degrees

Let's Try Together

Everyone find: sin 45 degrees

Steps:

1. Press sin
2. Enter 45
3. Press = or EXE

Answer: ≈ 0.7071

Did everyone get this?

More Practice

Try these on your calculator:

• cos 60 degrees
• tan 45 degrees

Answers:

• cos 60 degrees ≈ 0.5
• tan 45 degrees = 1

Building a Reference Table

Special Values to Remember

• sin 30 degrees = 0.5 (exactly!)
• cos 60 degrees = 0.5 (exactly!)
• tan 45 degrees = 1 (exactly!)
• sin 45 degrees = cos 45 degrees ≈ 0.707

Practice Problems

Find these values (round to 3 decimal places):

1. sin 20 degrees
2. cos 75 degrees
3. tan 50 degrees

Answers

1. sin 20 degrees ≈ 0.342
2. cos 75 degrees ≈ 0.259
3. tan 50 degrees ≈ 1.192

Pair Activity

Partner A: Call out angle and ratio
Example: "sin 35 degrees"

Partner B: Find value on calculator

Check together, then swap roles!

Word Problem 1

Question: In a right triangle, one angle is 40 degrees. If the hypotenuse is 10 cm, what is the opposite side?

Solution: Use sin!
opposite = hypotenuse × sin 40 degrees
opposite = 10 × 0.643
opposite ≈ 6.43 cm

Word Problem 2

Question: Angle is 55 degrees, adjacent is 8 cm. Find the opposite side.

Solution: Use tan!
opposite = adjacent × tan 55 degrees
opposite = 8 × 1.428
opposite ≈ 11.42 cm

Patterns to Notice

As angle increases from 0 to 90 degrees:

• sin goes from 0 to 1
• cos goes from 1 to 0
• tan goes from 0 to infinity

Important Notes

✓ sin and cos are always between 0 and 1 (for 0-90 degrees)
✓ tan can be larger than 1
✓ tan 90 degrees is undefined (calculator shows error)

Calculator Tips

1. Always check mode - must be DEG!
2. Write down enough decimal places
3. Round at the END of calculations, not in the middle
4. Different calculators may have different button orders

Exit Questions

Use your calculator to find (3 decimal places):

1. sin 25 degrees
2. cos 80 degrees
3. tan 38 degrees

Answers

1. sin 25 degrees ≈ 0.423
2. cos 80 degrees ≈ 0.174
3. tan 38 degrees ≈ 0.781

Homework

1. Create table: angles 10, 20, 30, 40, 50, 60, 70, 80 degrees
   Find sin, cos, tan for each

2. Solve triangle problems using calculator

3. Pattern investigation:
   Compare sin 20 degrees and cos 70 degrees
   What do you notice?

Next Lesson

Lesson 5: Finding Angles from Ratios

• Working backwards!
• If sin theta = 0.5, what is theta?
• Inverse functions: sin⁻¹, cos⁻¹, tan⁻¹

Credits

Created: December 2025
Based on: NCDC Lower Secondary Mathematics Syllabus (2019)

Source: National Curriculum Development Centre (NCDC), Uganda