Domain Restrictions of Tan, Cot, Sec, and Csc

Domain Restrictions of Tan, Cot, Sec, and Csc

What is it?

y = tan x: x != pi/2 + k pi. y = 4 tan(pi x): set pi x = pi/2 + k pi, x = 12 + k. y = csc 4x: 4x != k pi, x != k pi/4.

In simple words

• y = tan x: x != pi/2 + k pi.
• cos(inside)=0 for tan,sec
• sin(inside)=0 for cot,csc
• State the rule, show the working, and check the answer.

Important terms

DOMAIN RESTRICTIONS OF TAN, COT, SEC, AND CSC: y = tan x: x != pi/2 + k pi. y = 4 tan(pi x): set pi x = pi/2 + k pi, x = 12 + k. y = csc 4x: 4x != k pi, x != k pi/4.

HOLES: y = tan x: x != pi/2 + k pi.

What you should learn

• State the rule or meaning of domain restrictions of tan, cot, sec, and csc in easy words.
• Apply domain restrictions of tan, cot, sec, and csc in a clear step-by-step solution.
• Check the conditions, working, and final answer for accuracy.

Examples

• cos(inside)=0 for tan,sec
• sin(inside)=0 for cot,csc
• Solve for x

MAIN IDEA

y = tan x: x != pi/2 + k pi. y = 4 tan(pi x): set pi x = pi/2 + k pi, x = 12 + k. y = csc 4x: 4x != k pi, x != k pi/4.

EXAM USE

Write the rule first: y = tan x: x != pi/2 + k pi. Substitute carefully, show one step per line, and check signs, restrictions, units, and the final result.

Full school-level explanation

y = tan x: x != pi/2 + k pi. y = 4 tan(pi x): set pi x = pi/2 + k pi, x = 12 + k. y = csc 4x: 4x != k pi, x != k pi/4.

Understand the idea, then apply it:

WHAT — DOMAIN RESTRICTIONS OF TAN, COT, SEC, AND CSC

y = tan x: x != pi/2 + k pi. y = 4 tan(pi x): set pi x = pi/2 + k pi, x = 12 + k. y = csc 4x: 4x != k pi, x != k pi/4.

WHY — Why it matters

This rule is a separate learning unit inside tan, cot, sec, csc — domain holes. It can be defined, applied, and checked in its own FBISE question.

HOW — How to answer

Write the rule first: y = tan x: x != pi/2 + k pi. Substitute carefully, show one step per line, and check signs, restrictions, units, and the final result.

MAIN IDEA

y = tan x: x != pi/2 + k pi. y = 4 tan(pi x): set pi x = pi/2 + k pi, x = 12 + k. y = csc 4x: 4x != k pi, x != k pi/4.

Remember

• set inside = a hole of the parent

Examples

• cos(inside)=0 for tan,sec
• sin(inside)=0 for cot,csc
• Solve for x

EXAM USE

Write the rule first: y = tan x: x != pi/2 + k pi. 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 domain restrictions of tan, cot, sec, and csc 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

• set inside = a hole of the parent
• tan undefined at odd multiples of pi/2
• sec, csc miss (-1,1)
• tan all R, sec |y|>=1
• set inside = a hole of the parent
• focused answer
• accurate support
• set inside = a hole of the parent

Deeper understanding

Go beyond memorising Domain Restrictions of Tan, Cot, Sec, and Csc. 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

• set inside = a hole of the parent
• tan undefined at odd multiples of pi/2
• sec, csc miss (-1,1)
• tan all R, sec |y|>=1
• DOMAIN RESTRICTIONS OF TAN, COT, SEC, AND CSC: y = tan x: x != pi/2 + k pi. y = 4 tan(pi x): set pi x = pi/2 + k pi, x = 12 + k. y = csc 4x: 4x !=
• HOLES: y = tan x: x != pi/2 + k pi.

tan's range is all reals. sec's range is not. Do not mix them.

For long answers on Domain Restrictions of Tan, Cot, Sec, and Csc: define clearly → explain the main parts → give one example → state one exam caution.