Domain Restrictions of Tan, Cot, Sec, and Csc
y = tan x: x != pi/2 + k pi.
Learning objectives
- 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.
Definition
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.
Mathematical form
y = tan x
y = 4 tan(pi x)
x = pi/2 + k pi
x = 12 + k. y
Where / symbols
- 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 = 1/2 + k. y = csc 4x: 4x != k pi, x != k pi/4.
- HOLES
- y = tan x: x != pi/2 + k pi.
Relationship
- set inside = a hole of the parent
Overview
Understand the idea, then apply it:
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.
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.
Examples State the central idea · Use one accurate detail · Check the final response
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.
How to answer a domain restrictions of tan, cot, sec, and csc 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
tan's range is all reals. sec's range is not. Do not mix them.
Key points
- set inside = a hole of the parent
- tan undefined at odd multiples of pi/2
- sec, csc miss (-1,1)
- focused answer
Exam preparation
Exam Focus
Quick revision
Revision Zone
Domain Restrictions of Tan, Cot, Sec, and Csc
Sticky Notes · Quick Revision
Core Idea
- y = tan x: x != pi/2 + k pi.
What to Know
- 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.
Example or Evidence
- cos(inside)=0 for tan,sec
- sin(inside)=0 for cot,csc
- Solve for x
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.
Common Error
- tan's range is all reals. sec's range is not. Do not mix them.
FBISE Exam Check
- State the rule, show the working, and check the answer.
60-second revision
- 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.
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