Signs

Signs

What is it?

The reference angle is the acute angle to the x-axis. Quadrant II: 180 - theta. Quadrant III: theta - 180. Quadrant IV: 360 - theta. ASTC (or CAST): All sine cosine tangent positive in Q1; sine (and cosec) in Q2; tangent (and cot) in Q3; cosine (and sec) in Q4.

In simple words

• The reference angle is the acute angle to the x-axis.
• reference to the x-axis
• ASTC signs

Important terms

Signs: The reference angle is the acute angle to the x-axis. Quadrant II: 180 - theta. Quadrant III: theta - 180. Quadrant IV: 360 - theta. ASTC (or CAST): All sine cosine tangent positive in Q1; sine (and cosec) in Q2; tangent (and cot) in Q3; cosine (and sec) in Q4.

What you should learn

• Define and explain signs.
• Apply signs to a focused FBISE question.
• Check the answer for correct terms, evidence, working, and units.

Examples

• reference to the x-axis
• ASTC signs
• Define first

CORE UNDERSTANDING

The reference angle is the acute angle to the x-axis. Quadrant II: 180 - theta. Quadrant III: theta - 180. Quadrant IV: 360 - theta. ASTC (or CAST): All sine cosine tangent positive in Q1; sine (and cosec) in Q2; tangent (and cot) in Q3; cosine (and sec) in Q4.

EXAM APPLICATION

State the correct term, connect it to the chapter rule or evidence, and use a clear example or calculation.

Full school-level explanation

The reference angle is the acute angle to the x-axis. Quadrant II: 180 - theta. Quadrant III: theta - 180. Quadrant IV: 360 - theta. ASTC (or CAST): All sine cosine tangent positive in Q1; sine (and cosec) in Q2; tangent (and cot) in Q3; cosine (and sec) in Q4.

Learn the idea, then use it:

WHAT — SIGNS

The reference angle is the acute angle to the x-axis. Quadrant II: 180 - theta. Quadrant III: theta - 180. Quadrant IV: 360 - theta. ASTC (or CAST): All sine cosine tangent positive in Q1; sine (and cosec) in Q2; tangent (and cot) in Q3; cosine (and sec) in Q4.

HOW — Use the idea

Identify what is given, select this topic's rule or evidence, apply it one step at a time, and check the result.

CORE UNDERSTANDING

The reference angle is the acute angle to the x-axis. Quadrant II: 180 - theta. Quadrant III: theta - 180. Quadrant IV: 360 - theta. ASTC (or CAST): All sine cosine tangent positive in Q1; sine (and cosec) in Q2; tangent (and cot) in Q3; cosine (and sec) in Q4.

Remember

• reference to the x-axis
• ASTC signs

Examples

• reference to the x-axis
• ASTC signs

EXAM APPLICATION

State the correct term, connect it to the chapter rule or evidence, and use a clear example or calculation.

Remember

• correct term
• chapter link
• clear application

Examples

• Define first
• Show the rule or evidence
• Check units, labels, and conclusion

Remember

• reference to the x-axis
• ASTC signs
• keep the ideas separate
• reference to the x-axis
• ASTC signs
• correct term
• chapter link
• clear application

Deeper understanding

Go beyond memorising Signs. Connect the definition to reasons, relationships, exceptions, and exam wording.

Common mistakes

Exam focus

Core Idea

Key Points

Simple Check

How to Answer

Exam focus

Quick revision

• reference to the x-axis
• ASTC signs
• keep the ideas separate
• Signs: The reference angle is the acute angle to the x-axis. Quadrant II: 180 - theta. Quadrant III: theta
• WHAT — SIGNS: The reference angle is the acute angle to the x-axis. Quadrant II: 180 - theta. Quadrant III: theta
• HOW — Use the idea: Identify what is given, select this topic's rule or evidence, apply it one step at a time, and check

Do not merge signs with a neighbouring idea that uses a different definition, rule, or method.

For long answers on Signs: define clearly → explain the main parts → give one example → state one exam caution.