Sine
Positive for angles between 90° and 180°.
🎯 Learning Objectives
- interpret sine and cosine of obtuse angles;
- use calculator values correctly;
- convert decimal degrees to degrees and minutes;
- convert degrees and minutes to decimal degrees.
Introduction
This lesson develops Obtuse Angles and Degree–Minute Form from meaning and patterns before moving to calculations. Look for what the quantities, shapes or symbols represent, then connect that idea to the method.
Key Notes
Read the definitions and key facts below carefully. Each rule is most useful when you can explain why it fits the situation, not simply recall it.
Obtuse Angles
Cosine
Negative for angles between 90° and 180°.
Tangent
Negative for angles between 90° and 180°.
Degrees and Minutes
1 degree=60 minutes.
Convert 37.4°.
Whole degrees=37°.
0.4×60=24 minutes.
37.4°=37°24′
Convert 52°18′.
18÷60=0.3°.
52°18′=52.3°
Worked Examples
Reason through the method
- Identify the known information and what must be found.
- Choose the definition, property or formula that connects them.
- Substitute carefully and show each step.
- Check the notation, units and whether the result is sensible.
Practice Questions
- Convert 64.75° to degrees and minutes.
- Convert 28°42′ to decimal degrees.
- State the sign of cos120°.
- Explain why a negative cosine value can be valid.
✅ Check Your Work
Show answers and working
- 0.75×60=45, so 64°45′.
- 42÷60=0.7, so 28.7°.
- Negative.
- Cosine is negative in the second quadrant, where angles are obtuse.
🧭 Interactive Lab: Degrees and Minutes Converter
Change the values or make a choice and watch the mathematics respond.
Summary
📘 Remember
- Label the triangle before choosing a formula.
- Use degree mode unless the question says otherwise.
- Keep full calculator values until the final rounding step.
⚠️ Common Mistakes
- Using the wrong reference angle.
- Rounding too early.
- Forgetting units or the degree symbol.
⭐ Exam Tips
- Write the formula before substituting.
- Sketch and label any diagram that is not already provided.
- Check whether the answer is sensible for the shape.
🌍 Did You Know?
Surveyors, engineers, pilots and architects use trigonometry to calculate distances that are difficult or unsafe to measure directly.
Common Mistakes
- Choosing a rule before identifying what the question describes.
- Skipping working or changing notation part-way through a solution.
- Accepting an answer without checking its size, sign or units.
Exam Focus
Show the mathematical relationship you are using, keep notation consistent and give a clear final answer. Use a quick estimate, diagram or inverse operation to check that the result is reasonable.