Secant Definition and 58 Threads

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?