- #1
cscott
- 778
- 1
How can I use trig identities to let me differentiate [itex]\sin \left ( x + \frac{\pi}{2} \right)[/itex] and [itex]3 \sin x - 2 \cos x[/itex]?
Differentiating Trig Identities: Example
- Context: Undergrad
- Thread starter cscott
- Start date
Click For Summary
Discussion Overview
The discussion revolves around the differentiation of trigonometric functions, specifically \(\sin \left ( x + \frac{\pi}{2} \right)\) and \(3 \sin x - 2 \cos x\). Participants explore the use of trigonometric identities in the differentiation process.
Discussion Character
- Technical explanation, Conceptual clarification, Debate/contested
Main Points Raised
- One participant inquires about using trigonometric identities to differentiate specific functions.
- Another participant mentions the identity for \(\sin{(\alpha+\beta)}\) but questions the necessity of using it for differentiation.
- A third participant points out that \(\sin \left ( x + \frac{\pi}{2} \right) = \cos x\) and suggests that differentiating \(3 \sin x - 2 \cos x\) can be done directly without identities.
- One participant expresses realization about their initial approach after receiving clarification.
- Another participant asserts that trigonometric identities are not needed for differentiating the given functions.
Areas of Agreement / Disagreement
Participants generally agree that trigonometric identities are not necessary for differentiating the functions in question, though there is some debate about the utility of using identities in this context.
Contextual Notes
Some assumptions about the familiarity with trigonometric identities and differentiation techniques may be present, but these are not explicitly stated.
- #2
Jameson
- 4,533
- 13
Well, there's an identity for [tex]\sin{(\alpha+\beta)}[/tex] but why would you want to use it? Those can be differentiated easily... I'm missing something.
- #3
TD
Homework Helper
- 1,016
- 0
Well, [itex]\sin \left ( x + \frac{\pi}{2} \right) = \cos x[/itex] if that helps 
I don't see why you'd want to change the second one though, taking the derivative is lineair so [itex]\left( {3\sin x - 2\cos x} \right)^\prime = 3\left( {\sin x} \right)^\prime - 2\left( {\cos x} \right)^\prime[/itex]
I don't see why you'd want to change the second one though, taking the derivative is lineair so [itex]\left( {3\sin x - 2\cos x} \right)^\prime = 3\left( {\sin x} \right)^\prime - 2\left( {\cos x} \right)^\prime[/itex]
- #4
cscott
- 778
- 1
Damn, I guess I wasn't looking at them right. Thanks.
- #5
Hurkyl
Staff Emeritus
Science Advisor
Gold Member
- 14,922
- 28
You don't need trig identities to differentiate those...
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