Can someone explain to me how logarithmic differentiation for the trig functions (Sin, Cosine, Tangent, Secant, Cosecant, Cotangent) are derived?
For instance, one of these problems that involves trig functions is:
(Note: I am using the "@" symbol in place of theta, so the problem reads as y = theta + 5/ theta*cos*theta)
y = @ + 5/ @cos@
I know the first step is:
lny = ln(@+5) -ln@ - ln(cos@)
What I don't get is how they are saying (in my student solution's manual) that the natural log of -ln(cos@) is + sin@/cos@, which the next step shows:
1/y dy/d@ = 1/(@ + 5) - 1/@ + sin@/cos@
I don’t get how they are getting this, as I thought it would simply be -1/cos@, or –sec@.
Can someone explain to me why this is the case for the cosine, and how the natural logs of the other five trig functions are derived and what they are as well? It would be very helpful.
2007-03-20
19:35:32
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4 answers
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asked by
Ryan_1770
1
in
Mathematics