What simpler indentity is equal to sin(x) - cos(x)

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Discussion Overview

The discussion revolves around the question of whether there exists a simpler identity equivalent to the expression sin(x) - cos(x). Participants explore various approaches to this trigonometric expression, including potential transformations and applications in physics problems.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant asserts that there is no simpler identity for sin(x) - cos(x) and suggests plotting the curves to observe their differences.
  • Another participant proposes using an approximation or squaring both sides of the equation to manipulate the expression.
  • A different approach is introduced using the cosine addition formula, leading to the expression sin(x) - cos(x) = -sqrt(2)cos(x+y) with y set to 45 degrees.
  • There is a correction regarding the expression, suggesting it should be sin(x) - cos(x) = sqrt(2)cos(x+45).
  • One participant expresses confusion about how to solve for theta in a physics context involving this identity.

Areas of Agreement / Disagreement

Participants do not reach a consensus on whether a simpler identity exists, with differing opinions on the manipulation and interpretation of the expression sin(x) - cos(x).

Contextual Notes

Some participants reference specific trigonometric identities and transformations, but the discussion does not resolve the mathematical steps or assumptions involved in these transformations.

Who May Find This Useful

This discussion may be of interest to those studying trigonometric identities, particularly in the context of physics problems, as well as individuals seeking clarification on related mathematical concepts.

Matt Jacques
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What simpler indentity is equal to sin(x) - cos(x) ?

Trig Identities have come back to haunt me!
 
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Originally posted by Matt Jacques
What simpler indentity is equal to sin(x) - cos(x) ?

Trig Identities have come back to haunt me!

There isn't one. Plot out the two curves and look at their differences and you'll see it's not simpler than the basic sine curve.

There are lots of websites to check out trig identities if you need references. A quick google search will show more than you need, but most contain the same information. Here's three is you want to check them out:

http://www.math2.org/math/trig/identities.htm

http://aleph0.clarku.edu/~djoyce/java/trig/identities.html

http://www.mathwizz.com/algebra/help/help32.htm
 
Then how do I solve for theta in a physics problem that contains that identity?
 
Approximation? Square both sides of the equation (to get sin^2(x) + cos^2(x) - 2sin(x)cos(x) = 1 - sin(2x))? You're being much too vague ;)
 
cos(x+y)=cos(x)cos(y)-sin(x)sin(y). Lety=45o. Net result
sin(x)-cos(x)=-sqrt(2)cos(x+y).

Is that simple enough?
 
Originally posted by mathman
cos(x+y)=cos(x)cos(y)-sin(x)sin(y). Lety=45o. Net result
sin(x)-cos(x)=-sqrt(2)cos(x+y).

Is that simple enough?

Just nitpicking -- shouldn't that be

[tex]\sin(x)-\cos(x)=\sqrt{2}\cos(x+45)[/tex]
 
Thanks everyone!
 
need a help with log problem

I'm a bit confused with this problem can you help me to workout and explain it to me on the way. thanks.

log(e)x=a log(e0y=c express log(e){(100x^3y^-1/2)/(y^2)} in terms of a and c.

my interpretation is that you separate the function then workout by using loga(mn)=logam+logan law. thanks for your guys.
 
Is it
[tex]\log(\frac{100x^3y^{\frac{-1}{2}}}{y^2})[/tex]
 
Last edited:
  • #10
jcm; you should start a new post when you want to ask an unrelated question.
 
  • #11
If I read your equations correctly, it should be ln100+3a-(5/2)c
 

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