- #1
cscott
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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
- Thread starter cscott
- Start date
In summary, the conversation discusses using trig identities to differentiate \sin \left ( x + \frac{\pi}{2} \right) and 3 \sin x - 2 \cos x. However, it is noted that these can be differentiated easily without using trig identities.
- #2
Jameson
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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
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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
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Damn, I guess I wasn't looking at them right. Thanks.
- #5
Hurkyl
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You don't need trig identities to differentiate those...
What is the purpose of differentiating trig identities?
Differentiating trig identities allows us to find the derivatives of trigonometric functions, which is useful in various areas of science and engineering.
What is an example of differentiating a trig identity?
An example of differentiating a trig identity is finding the derivative of sin(x):
d/dx(sin(x)) = cos(x)
What is the chain rule in differentiating trig identities?
The chain rule is used when differentiating composite trig identities, where the function inside the trigonometric function is a function of another variable.
What are the common trig identities used in differentiation?
Some common trig identities used in differentiation include the power rule, product rule, quotient rule, and chain rule.
How can differentiating trig identities be applied in real life?
Differentiating trig identities has practical applications in fields such as physics, engineering, and economics, where trigonometric functions are used to model various phenomena.
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