Topic 1805 min read
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.
Choose Your Level
180 and Cast
What is it?
Second quadrant: sine +. sin(180-A)=+sin A. cos(180-A)=-cos A. Third: tan +. Fourth: cos +. Draw a quick CAST if needed.
In simple words
- Second quadrant: sine +.
- 180-A: sin +
- 180+A: both sin and cos -
- State the rule, show the working, and check the answer.
Important terms
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 +.
What you should learn
- 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.
Examples
- 180-A: sin +
- 180+A: both sin and cos -
- 360-A: cos +
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.
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.
Recommended for Class 11
Full school-level explanation
Second quadrant: sine +. sin(180-A)=+sin A. cos(180-A)=-cos A. Third: tan +. Fourth: cos +. Draw a quick CAST if needed.
Understand the idea, then apply it:
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.
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.
Remember
- ASTC / CAST
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.
Remember
- focused answer
- accurate support
Examples
- State the central idea
- Use one accurate detail
- Check the final response
How to answer a 180 and cast question
How it works
- 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.
Remember
- ASTC / CAST
- reduce to A, then sign from the quadrant
- sin(90-A)=cos A
- sine + in Q2
- ASTC / CAST
- focused answer
- accurate support
- ASTC / CAST
Deeper understanding
Go beyond memorising 180 and Cast. Connect the definition to reasons, relationships, exceptions, and exam wording.
Common mistakes
Exam focus
Core Idea
What to Know
Example or Evidence
How to Answer
Exam focus
Quick revision
- ASTC / CAST
- reduce to A, then sign from the quadrant
- sin(90-A)=cos A
- sine + in Q2
- 180 AND CAST: Second quadrant: sine +. sin(180-A)=+sin A. cos(180-A)=-cos A. Third: tan +. Fourth: cos +. Draw a q
- 180 AND CAST: Second quadrant: sine +.
sin(180-A)=+sin A, but cos(180-A)=-cos A. Do not give both a plus.
For long answers on 180 and Cast: define clearly → explain the main parts → give one example → state one exam caution.
Exam Focus
Exam Focus
Important points
- ASTC / CAST
- reduce to A, then sign from the quadrant
- sin(90-A)=cos A
- sine + in Q2
Important formulas
- ASTC / CAST
- reduce to A, then sign from the quadrant
- sin(90-A)=cos A
Common exam traps
- sin(180-A)=+sin A, but cos(180-A)=-cos A. Do not give both a plus.
- Do not choose a formula before checking that its conditions fit the question.
Long question structure
Definition → key parts → example → exam caution
Common Mistakes
Common Mistakes
- Mistake
sin(180-A)=+sin A, but cos(180-A)=-cos A. Do not give both a plus.
- Mistake
Do not choose a formula before checking that its conditions fit the question.
- Mistake
Do not hide sign changes, restrictions, or skipped algebra steps.
- Mistake
sin(180-A)=+sin A, but cos(180-A)=-cos A. Do not give both a plus.
Revision Zone
60-Second Revision
Quick cues from this topic — use them for last-minute revision.
ASTC / CAST
reduce to A, then sign from the quadrant
sin(90-A)=cos A
sine + in Q2
Second quadrant: sine +. sin(180-A)=+sin A. cos(180-A)=-cos A. Third: tan +. Fourth: cos +. Draw a quick CAST if needed.
sin(90-A)=cos A
- Definition
- Second quadrant: sine +. sin(180-A)=+sin A. cos(180-A)=-cos A. Third: tan +. Fourth: cos +. Draw a quick CAST if needed.
- Formula
- sin(90-A)=cos A
- Example
- 180-A: sin +
- Critical warning
- sin(180-A)=+sin A, but cos(180-A)=-cos A. Do not give both a plus.
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Exam Practice
Define
Q1. Define 180 and Cast.
Explain
Q2. Explain: MAIN IDEA.
Example
Q3. Give one clear example of 180 and Cast and say why it fits.
Mistake
Q4. State one common mistake students make about 180 and Cast.
Exam note
Q5. Write a short exam note on 180 and Cast: definition, two points, one example.
Sources & References
School-standard facts for Matric and Intermediate. Original explanations — not copied from textbooks.