90 Minus

90 Minus

What is it?

sin(90-A)=cos A, cos(90-A)=sin A, tan(90-A)=cot A. Complementary. Use to rewrite.

In simple words

• sin(90-A)=cos A, cos(90-A)=sin A, tan(90-A)=cot A.
• sin(90-A)=cos A
• sec(90-A)=csc A
• State the rule, show the working, and check the answer.

Important terms

90 MINUS: sin(90-A)=cos A, cos(90-A)=sin A, tan(90-A)=cot A. Complementary. Use to rewrite.

90 MINUS: sin(90-A)=cos A, cos(90-A)=sin A, tan(90-A)=cot A.

What you should learn

• State the rule or meaning of 90 minus in easy words.
• Apply 90 minus in a clear step-by-step solution.
• Check the conditions, working, and final answer for accuracy.

Examples

• sin(90-A)=cos A
• sec(90-A)=csc A
• Same idea pi/2 - A

MAIN IDEA

sin(90-A)=cos A, cos(90-A)=sin A, tan(90-A)=cot A. Complementary. Use to rewrite.

EXAM USE

Write the rule first: sin(90-A)=cos A, cos(90-A)=sin A, tan(90-A)=cot A. Substitute carefully, show one step per line, and check signs, restrictions, units, and the final result.

Full school-level explanation

sin(90-A)=cos A, cos(90-A)=sin A, tan(90-A)=cot A. Complementary. Use to rewrite.

Understand the idea, then apply it:

WHAT — 90 MINUS

sin(90-A)=cos A, cos(90-A)=sin A, tan(90-A)=cot A. Complementary. Use to rewrite.

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: sin(90-A)=cos A, cos(90-A)=sin A, tan(90-A)=cot A. Substitute carefully, show one step per line, and check signs, restrictions, units, and the final result.

MAIN IDEA

sin(90-A)=cos A, cos(90-A)=sin A, tan(90-A)=cot A. Complementary. Use to rewrite.

Remember

• complement

Examples

• sin(90-A)=cos A
• sec(90-A)=csc A
• Same idea pi/2 - A

EXAM USE

Write the rule first: sin(90-A)=cos A, cos(90-A)=sin A, tan(90-A)=cot A. 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 90 minus 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

• complement
• reduce to A, then sign from the quadrant
• sin(90-A)=cos A
• sine + in Q2
• complement
• focused answer
• accurate support
• complement

Deeper understanding

Go beyond memorising 90 Minus. 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

• complement
• reduce to A, then sign from the quadrant
• sin(90-A)=cos A
• sine + in Q2
• 90 MINUS: sin(90-A)=cos A, cos(90-A)=sin A, tan(90-A)=cot A. Complementary. Use to rewrite.
• 90 MINUS: sin(90-A)=cos A, cos(90-A)=sin A, tan(90-A)=cot A.

sin(180-A)=+sin A, but cos(180-A)=-cos A. Do not give both a plus.

For long answers on 90 Minus: define clearly → explain the main parts → give one example → state one exam caution.