Hi,
We were going over trigonometric integration in Calculus II the other day. I got the basic idea, but get lost when we're doing the u-substitution.
We had a problem like this:
\int cos^3 (x) dx
Then we did:
\int (1 - sin^2 (x)) cos(x) dx
Starting u-substitution:
u =...
y = sin( 4 x ) cos( 3 x )
f(x) = sin4x
g(x) = cos3x
f'(x) = cos4x
g'(x) = -sin3x
And by using the product rule, i'll get:
cos4x(cos3x) - sin4x(sin3x)
Is the answer correct or can be simplify again??
Homework Statement
If cos x = a/b and tan x = c/d; where a, b, c do not equal 0, then sin x is...
(a) bd/ac
(b) bc/ad
(c) ad/bc
(d) ad/bc
Homework Equations
The Attempt at a Solution
The way I see it, if cos x = a/b, then b=hypotenuse.
if tan x = c/d, then d=...
Homework Statement
The graphs of f( ) = 2sin() - 1 (blue) , and g() = 3cos() + 2 (red)
are shown below:
http://img403.imageshack.us/img403/6991/38ah7.jpg
http://g.imageshack.us/g.php?h=403&i=38ah7.jpg
What equation would have the intersection points of the graph its solutions...
Homework Statement
∫sec^2 (x) * tan (x) dx
Homework Equations
sec^2 (x)= 1+tan^2(x)
The Attempt at a Solution
=∫(1+tan^2 (x) or tan (x) tan (x)) tan (x) dx u=tan x, du=sec^2 dx
∫ (1+u^2) u du
= ∫u+u^2)du
= u^2/2 + u^3/3 = 1/2 tan^2(x)+ 1/3 tan^3 (x) +c
the...
Homework Statement
∫ cosx+sin 2X/sinX
Homework Equations
sin^2 x =1/2 (1-cos2x), cos^2=1/2 (1+cos2x)
if cosine is odd, u sin x, cos^2 x=1-sin^x) , if sine is odd u=cosx sin^2x =1-cos^2x)
The Attempt at a Solution
i'm not sure how to start this one because I've never came...
Homework Statement
∫1/x^2*√25-x^2
Homework Equations
√a^2-x^2 , x=a sin (theta) , -pi/2 less than or equal theta less than or equal pi/2 Identity 1-sin^2 theta= cos^2 theta
table of trigonometric substitutions
The Attempt at a Solution
x=5 sin theta
dx= 5...
Homework Statement
http://img206.imageshack.us/img206/9099/titleol2.jpg
http://g.imageshack.us/g.php?h=206&i=titleol2.jpg
Show the above statement is equivalent to : sec (2x) + tan (2x)
Homework Equations
The Attempt at a Solution
First attempt in which I used the...
Homework Statement
Verify the possibility of an identity graphically. (Completed this part)
Then, prove each identity algebraically.
\dfrac{sinx+tanx}{cosx+1}=tanx
Homework Equations
tan\theta=\dfrac{sin\theta}{cos\theta}
cot\theta=\dfrac{cos\theta}{sin\theta}...
Homework Statement
2 cos^2 x + cos x = 0
and
tan x = 3^1/2
Homework Equations
.. ?? Unit circle.
The Attempt at a Solution
for the first, well I tried factoring to isolate x, but it really did not work
i keep making up my own rules that end up messing with the entire equation...
Homework Statement
1/\sqrt{}2 cos 15 - 1/\sqrt{}2 sin 15
The Attempt at a Solution
I got \sqrt{}3/2.
If anyone could confirm this, I would appreciate it. Thanks.
I need to solve for x, but,..
honestly, i haven't got a clue for where to begin, or
even,.. oy, not sure
here are two of my problems:
sin x = (3^1/2) / 2
and
2 cos 2 x + cos x = 0
I know I'm supposed to use the unit circle,.. well, maybe
any help at all would be very much...
Can someone please give me some tips on how to solve this? :
400*(2,2*cosV-1)*tanV=20*9,81, I am supposed to find V, but I can't see how to solve this equation.
Evaluate sin(tan^{-1}(\frac{1}{3}))
3. The Attempt at a Solution
Let y = tan^{-1}(\frac{1}{3})
<=> tan(y)=1/3
y = ?
sin(tan^{-1}(\frac{1}{3})) = sin y
I think for solution to exist tan^{-1}(\frac{1}{3}) must be in the range of sin, (that is \left\frac{-\pi}{2}...
Homework Statement
I'm learning now about darivative all by my self (without a teacher) and I'm not sure about this development
Homework Equations
The Attempt at a Solution
Y=senx
y+{\Delta}Y=sen(x+{\Delta}Y)
{\Delta}Y=senx*cos{\Delta}x+ sen{\Delta}x*cosx
What about...
Homework Statement
Find I = \int_0^{2\pi} \frac{1}{cos\phi+b} d\phi
Homework Equations
Given above..
The Attempt at a Solution
This problem is an introductory problem to trigonometric functions and here is how the answer is obtained - but I have a question about it. First, here...
The question is:
Use x = \tan \theta , \frac{-\pi}{2} < \theta < \frac{\pi}{2} to show that:
\int_{0}^{1} \frac{x^3}{\sqrt{x^2+1}} dx =\int_{0}^{\frac{\pi}{4}} \tan^3 \theta \sec \theta d\theta
Using that substitution, I got it down to:
\int_{0}^{\frac{\pi}{4}} \frac{\tan^3...
Homework Statement
I'm attempting to prove that
1 - sin^2 t /(1 + cos t) - cos^2/(1+tan t) = cos t sin t
2. The attempt at a solution
I've tried various approaches. The most promising has the LHS reduced to:
(sin t cos t (1 + cos t + sin t cos t))/((1 + cos t)(cos t + sin t))...
Homework Statement
lim x --->0 [tan(2+x)^3 - tan8]/x
Homework Equations
f'(a)=lim h-->0 f(a+h)-f(a)/h
The Attempt at a Solution
should i differentiate first? am i allowed to do that?
Im supposed to verify that (1-sinx)/(1+sinx) = (secx-tanx)^2
RHS = (secx-tanx)^2 = (1/cosx - sinx/cosx)^2 = [(1-sinx) / cosx]^2
= [(1-sinx)(1-sinx)]/cosx^2 = (1-2sinx+sinx^2)/(1-sinx^2)
From here, I'm feeling pretty confused. I'm not even sure if all my values are correct.
Homework Statement
Given:
sin x + sin y= a
cos x + cos y=b
find tan(x+y)
Prove it to be equal to"
\frac{2ab}{b^{2}-a^{2}}
The Attempt at a Solution
I get stuck after this:
2ab= 2 sin (x+y)+sin 2x+sin 2y
b^{2}-a^{2}= cos 2x + cos 2y + 2 cos (x+y)
Division of the two never...
How do I find the derivative of cos2x?
Do I use the chain rule?
u=2x
u'=2
y=cosu
y'=-sinu
dy/dx=-2sin(2x)
Edit: Sorry. I mean derivative, not integral.
[SOLVED] Derivatives of Trigonometric Functions
I need to find the critical numbers of this function:
y = cos x - sin x where -pi <= x <= pi
I found the derivative as:
dy/dx = -(sin x + cos x)
But when I equate dy/dx to zero, I get:
sin x + cos x = 0...where do I go from here?
Hi there,
I am struggling to solve for x in the following problem:-
Find all values of x in the interval 0<= x <= 360 for which: tan^2(x) = 5sec(x) - 2
I have used the identity tan^2(x) + 1 = sec^2(x) to get:
sec^2(x) - 1 = 5sec(x) - 2
and rearranged to get
sec^2(x) - 5sec(x) +...
Homework Statement
Reduce the following series to the most simplified form:
1. 2 sin^{2}(\theta/2)*(1+cos\theta)*(1+cos^{2}\theta)(1+cos^{4}\theta)...
2. tan (\theta/2)*(1+sec \theta)(1+2\theta)(1+sec 4\theta).......
Homework Equations
For problem 1:
2...
Homework Statement
\int\frac{1+\sqrt{cosx}}{sinx} Hi , I really need a help for this
Homework Equations
The Attempt at a Solution
\int\frac{1+\sqrt{cosx}}{\sqrt{sin}\sqrt{sin}}
\int\frac{1}{sinx} + \int\frac{1}{\sqrt{sinx}}\sqrt{}\frac{cosx}{sinx} =
\int cscx +...
using those formulas, how would you solve
tan 11 pi
-----
8
and cot 195
also, how would you prove tan (x +y ) = tan x
and tan ( pi/4 -x) = 1 - tan x
---------
1 + tan x
thank you so much for any help
Homework Statement
Evaluate the Integral: Sqrt[(X^2)+9]
Homework Equations
I know its an Integration By parts problem, but I don't know how to start it.
The Attempt at a Solution
Im JUST learning this as I type this problem out, I've just been stuck on it for a while and my book...
Homework Statement
http://imageshack.us"
how are the solutions of the fourth roots pi/2? how do you get pi/2, you know the thing after "cos" and "isin" ?
0=-85.7cos(theta)+bcos30-85.7
0=-85.7sin(theta)+bsin30
Can someone please tell me what I am doing wrong.
theta=sin^-1(bsin30/85.7)
then sub that into the first equation.
I then solved the equation on my calculator and it gave me 9999999999 which i know is wrong.
Homework Statement
A = [ b c ... 0000000000000000000 ]
[ c b c ... .000000000000000 0]
[ ... ]
[ 000000000000000000 c b c ]
[ 000000000000000000 b c ]
where a,b are real. This matrix is tridigonal and symmetric.
I need to...
Homework Statement
Hey, it's me again. This method is giving me some trouble. This is the first problem: \int^3_0\ x^2\sqrt{9-x^2} \ dx
The second problem is:
\int\frac{dx}{\sqrt{2x^2+2x+5}}. How do I use a trig. substitution to start on this one?
Homework Equations
The Attempt at a...
Homework Statement
Hey folks, I believe I'm right in what I've done so far. I'm looking for confirmation of my methods and also wondering how to finish the first one by subbing in pi/6 for x and keeping pi in the answer. Thank you for your help. Cheers.
\int^{\frac{\pi}{6}}_0 sin^2(x)\ cos^3...
[SOLVED] Question involving trigonometric identities and inverse functions
Homework Statement
http://img141.imageshack.us/img141/2651/quiz1question5zi8.jpg
Homework Equations
I've tried to combine the following known equations to come up with a solution:
\frac{d}{dx}(sin^{-1}x) =...
I am not sure of the way in which I am solving. I am showing my approach and my questions are at end.
Plz advise why I maybe wrong?
Thanks
Asif
Problem Statement:
Use the formula for sum of a geometric progression to compute
exp(i\theta) + exp(i2\theta) +...+exp(in\theta)...
First I wanted to say hello, that I'm new to the forum, and very glad to have found you!
I am having a terrific time with verifying my trig identities. I have done ALL odd probs in my text, and am repeating them. The problem that I am having is that I do not see a clear path from one side of...
[SOLVED] Integration with Trigonometric Substitution
Homework Statement
Given integral (I):
I[(x)sqrt(9-x^2)dx]
by words:
Integral of "X" times square root of "9-X(squared)
Use proper trigonometric substitution to solve this problem.
Homework Equations
The Attempt at a Solution
I have a few quick problems concering evaluating integrals by trigonometric substitution. I guess I will just post five that way if anyone can help with any, would be greatly appreciated. Also: if anyone could inform me on how to input the actual equations onto this forum as I have seen in some...
Homework Statement
Integrate cos^n x cos nx
Homework Equations
Integration by part equations, trigonometric integrals
The Attempt at a Solution
I was given the hint that this integration involves integration by part and trigonometry integrals. I tried integration by part, by...
Homework Statement
The integral of cos[x]*(sin[x])^5dx
Homework Equations
The Attempt at a Solution
I split it into cos[x]*(sin[x])^2 * (sin[x])^2 * sin[x]
then each sin^2[x] term becomes (1-cos[x]^2)
so you end up with the integral of cos[x]*(1-cos[x]^2)^2*sin[x]dx
let...
[SOLVED] Trigonometric Transformation
This is a calculus 3 problem, but this part involves only trig identities:
Make the function f(x,t) = sin(t)*sin(x) into the form: f(x+t)+g(x-t).
I'm not sure whether to use half angle formulas, or what?
Hi, I had a question about the following problem:
http://calcchat.tdlc.com/solutionart/calc8e/01/c/se01c01067.gif
Can someone explain how sin(0)/0 = 1?
Why do some problems return the wrong answer while others do not on the ti-89.
For example:
\[ \lim_{x \to 0} \frac{\cos\theta \tan\theta}{\theta}\]
Shows up wrong (shows up as pi over 180).
But
\[ \lim_{x \to 0} \frac{\sin x(1 - \cos x)}{2x^2}\]
does not?