Inequalities with trigonometric functions

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Homework Help Overview

The discussion revolves around inequalities involving trigonometric functions, specifically focusing on the functions f(x) = cos(x), g(x) = sin(x), and h(x) = tan(x) within specified domains. Participants are tasked with finding the range of f and determining the values of p and q for the function h, given that its range is the same as that of g.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants explore the ranges of the functions based on their definitions and domains. Questions arise regarding the relationship between domain and range, with some participants suggesting that identical domains imply identical ranges, while others challenge this assumption. There is also discussion about specific values for p and q and their implications for the range of h.

Discussion Status

The discussion is ongoing, with participants questioning each other's reasoning and assumptions. Some have offered insights into the values of p and q, while others have raised concerns about the interpretation of the problem and the relationships between the functions. There is no explicit consensus yet, as different interpretations are being explored.

Contextual Notes

Participants note potential confusion regarding the use of degrees versus radians in the context of trigonometric functions. There is also mention of the need to clarify the relationship between the ranges of the functions and their respective domains.

tigerd12
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Homework Statement



Three functions are defined as follows:

f:x> cos x for the domain 0< (or equal to) x < (or equal to) 180
g:x> sin x for the domain 0< (or equal to) x < (or equal to) 90
h:x>tan x for the domain p< (or equal to) x < (or equal to) q


Find the range of f.

-1<(or equal to) x < (or equal to) 1 (correct?)

Given that the range of h is the same as the range of g, find a value of p and a value of q.

this is the one i don't quite understand, i got p = 0, q= 90, is that right?

if the domain is the same therefore the range is the same, yes?
 
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if the domain is the same therefore the range is the same, yes?
No, not necessarily. And, isn't the question "given identical ranges, find the domain of h"?
 
EnumaElish said:
No, not necessarily. And, isn't the question "given identical ranges, find the domain of h"?

Yes, so I am right. ?
 
Can you graph sin and tan between 0 and 360? Or between 0 and 90? What is Sin(0)? What is Sin(90)?

What is Tan(0)? Tan(90)?
 
Last edited:
tigerd12 said:

Homework Statement



Three functions are defined as follows:

f:x> cos x for the domain 0< (or equal to) x < (or equal to) 180
g:x> sin x for the domain 0< (or equal to) x < (or equal to) 90
h:x>tan x for the domain p< (or equal to) x < (or equal to) q
A bit peculiar, actually! I assume they mean 180 degrees, and 90 degrees.
Normally, sine and cosine, as functions are interpreted as in radians. The way sine and cosine are defined, as functions, x is "dimensionless" but radians give the correct values. Anyway, I'll go with degrees.


Find the range of f.

-1<(or equal to) x < (or equal to) 1 (correct?)

Given that the range of h is the same as the range of g, find a value of p and a value of q.

this is the one i don't quite understand, i got p = 0, q= 90, is that right?

if the domain is the same therefore the range is the same, yes?
When p= 0, tan(p)= 0. That's not what you want is it?
What is tan(90)? That's also not what you want is it?

For what p is tan(p)= -1?
For what q is tan(q)= 1?
 
I think I got it

Wait.. I think I got this..

so sin(0) - tan(0

sin(90) = 1
tan(45) = 1

therefore the P and Q are 0 and 45?
 
tigerd12 said:
Wait.. I think I got this..

so sin(0) - tan(0

sin(90) = 1
tan(45) = 1

therefore the P and Q are 0 and 45?
I'm sorry, how did we get to talking about sin(x)- tan(x)? I thought the question was about the range of tan(x).
"h:x>tan x for the domain p< (or equal to) x < (or equal to) q" and you were to find the domain given that the range was the same as the range of sin(x) (-1 to 1).
You said you thought the domain would be the same as long as the range was the same. That is certainly not true! Different functions can take different domains (x-value) to the same range (y-value).
Yes, it is true that tan(45)= 1 so the upper limit is 45. But since the lower limit on the range of sin(x) is -1, you need to determine where tan(x)= -1, not 0!
 
Last edited by a moderator:

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