MathematicsChapter 8: Fundamentals of Trigonometry
180 and Cast
Second quadrant: sine +.
Learning objectives
- State the rule or meaning of 180 and cast in easy words.
- Apply 180 and cast in a clear step-by-step solution.
- Check the conditions, working, and final answer for accuracy.
Definition
Second quadrant: sine +. sin(180-A)=+sin A. cos(180-A)=-cos A. Third: tan +. Fourth: cos +. Draw a quick CAST if needed.
Where / symbols
- 180 AND CAST
- Second quadrant: sine +. sin(180-A)=+sin A. cos(180-A)=-cos A. Third: tan +. Fourth: cos +. Draw a quick CAST if needed.
- 180 AND CAST
- Second quadrant: sine +.
Relationship
- sin(90-A)=cos A
Overview
Understand the idea, then apply it:
Main Idea
Second quadrant: sine +. sin(180-A)=+sin A. cos(180-A)=-cos A. Third: tan +. Fourth: cos +. Draw a quick CAST if needed.
Examples 180-A: sin + · 180+A: both sin and cos - · 360-A: cos +
Exam Use
Write the rule first: Second quadrant: sine +. Substitute carefully, show one step per line, and check signs, restrictions, units, and the final result.
Examples State the central idea · Use one accurate detail · Check the final response
WHAT — 180 AND CAST
Second quadrant: sine +. sin(180-A)=+sin A. cos(180-A)=-cos A. Third: tan +. Fourth: cos +. Draw a quick CAST if needed.
WHY — Why it matters
This rule is a separate learning unit inside allied angles. It can be defined, applied, and checked in its own FBISE question.
HOW — How to answer
Write the rule first: Second quadrant: sine +. Substitute carefully, show one step per line, and check signs, restrictions, units, and the final result.
How to answer a 180 and cast question
- Read the exact command word and identify what the question asks.
- State the matching idea, rule, or meaning before adding detail.
- Use the unit evidence or mathematical working that directly supports the answer.
- Check accuracy, relevance, and answer length before finishing.
In simple words
sin(180-A)=+sin A, but cos(180-A)=-cos A. Do not give both a plus.
Key points
- ASTC / CAST
- reduce to A, then sign from the quadrant
- sin(90-A)=cos A
- focused answer
Exam preparation
Exam Focus
Quick revision
Revision Zone
Review the key facts, formulas and checks before you move on.180 and Cast
Sticky Notes · Quick Revision
Core Idea
- Second quadrant: sine +.
What to Know
- Second quadrant: sine +. sin(180-A)=+sin A. cos(180-A)=-cos A. Third: tan +. Fourth: cos +. Draw a quick CAST if needed.
Example or Evidence
- 180-A: sin +
- 180+A: both sin and cos -
- 360-A: cos +
How to Answer
- Write the rule first: Second quadrant: sine +. Substitute carefully, show one step per line, and check signs, restrictions, units, and the final result.
Common Error
- sin(180-A)=+sin A, but cos(180-A)=-cos A. Do not give both a plus.
FBISE Exam Check
- State the rule, show the working, and check the answer.
60-second revision
- Second quadrant: sine +.
- 180-A: sin +
- 180+A: both sin and cos -
- State the rule, show the working, and check the answer.
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