this video is on trig identities
derivatives and integrals
as they apply to trig
functions
and let's get started
we have um
second alpha
allows you to put letters into the calculator or the screen I_n_d_e_x
alpha 8
closed parentheses, closed parentheses
tells you
uh... for calculus
and up comes a menu and we're going are you can go up and go down in the last
part of the
alphabet
and we want to go maybe
trig and half angle formulas for that
pretty interesting program
you can scroll down and choose whatever you want for instance lets start something
easy like cosine of x
and you notice the derivative of cosine of x minus sign of x and the integral
of cosine of x is sine of x plus c
identities or one over secant cotangent sine of x sine of x over tangent of x
double angle formula cosine of x equals sine of two x
divided by two sin of x
these are all things that come up in calculus
and you either memorize them or you know them
your a genius
or like me would trigger my mind once i get away from sin or cosine and um...
was able to
add the identity to come back and do some problems
lets take for instance the next one cosine squared of x
half angle formula his equal to one-plus cosine two x
divided by two pythagorean identity is one minus sine squared x
derivative
you have the original function cosine
squared of x which is really cosine of x times cosine of x
and so you have the product rule here which we use f prime then would be
cosine of x times
the derivative of cosine of x plus
the derivative cosine of x times cosine of x
and it works out to these
uh... cosine of x minus sign of x et-cetera et-cetera
and that's how they get the
derivative of two sine of x cosine of x pretty interesting
lets do one more
