Proving slope "m" of a secant connecting two points of the sine curve
Homework Statement
Write and expression for the slope m of the secant connecting the points Po(Xo,Yo) and P(X,Y) of the sine curve. Use the appropriate trigonometric identity to show that m= sin((X-Xo)/2)/((X-Xo)/2) * cos...
Homework Statement
(integrate)sec^3(2x)*tan(2x)dx
Homework Equations
The Attempt at a Solution
Okay, so first I tried to separate secant and tangent, to get (integrate)1/cos^3(2x) * sin(2x)/cos(2x)dx. The u would be cos(2x), the du would be -du=sin(2x)dx.
I subsitute these...
Homework Statement
Basically, I have to find
\int \frac{1}{cosx} dx
by multiplying the integrand by \frac{cosx}{cosx}
I go through and arrive at a solution, but when I differentiate it,
I get -tan(x)
something's clearly wrong, but I can't see what it is that I'm doing wrong...
Hello there
In the derivative of the arc secant, why is the absolute value of x ( which is present in the denominator) taken? Is this to prevent the possible of having a zero ( and making the whole expression undefined ? )
Thanks
For one of my homework assignments, I had to find the integral of a function. I got my function simplified to sec(t)^(8/3). I tried to use the reduction formula for sec(t)^n, but I believe that it only works if the power of sec is an integer. Could somebody help me out, please?
Edit: I...
Hello all, I have a question concerning the Tangent and Secant Functions (the graphs). I cannot think of a way that either of these can be used in the real world. I need to find applications for these. For example, the sine function can be used to represent waves or periodic motion... but...
\int \sec hx
I solve it in this way:
\int \arccos hx
\int \ln (x^2 + \sqrt{x^2 -1}) dx
Then, I substitute u = \ln (x + \sqrt{x^2 + 1})
then I get
x\ln(x + \sqrt{x^2 + 1}) - \int x/\sqrt{x^2 + 1}dx
and then I substitute v = x^2 + 1
x\ln(x + \sqrt{x^2 + 1}) -1/2 \int v^(1/2) dv...
I wrote down the notes from class, but when I tried to do the homework, I am not even close to the right answers. The formula I wrote down is:
\frac{-1}{(x)(x+h)}
Apparently that's wrong. Anyone know what it's supposed to be?