Trigonometric functions Definition and 165 Threads

The problem is as the title says. This is an example we went through during the lecture and therefore I have the solution. However there is a particular step in the solution which I do not understand. Using the Taylor series we will write sin(x) as: sin(x) = x - (x^3)/6 + (x^5)B(x) and...

I'm having a problem understanding exactly why trig functions are defined the way they are. Of course, the definition in terms of 0 to 90 degree angles within right triangles is easy: the functions just give the ratio of the sides given the angle. However, I don't understand how or why trig...

Can someone please explain to me why in this problem, for example, the sine and cosine functions are used in equating the force's components? I am having a hard time solving for these unknown forces because of my rusty trig skills. It asks to "determine the maximum weight of the flowerpot...

I'm not sure if this is the correct section for this thread since this isn't homework, but my question is very basic, so I think this section is suitable. I have two questions regarding the trigonometric functions (sinx,cosx,tanx etc). 1) What is the geometric meaning (i.e in the context...

Hi MHB, Solve $(2+ \sqrt{2})^{(\sin x)^2}-(2- \sqrt{2})^{(\cos x)^2}=\left( 1+ \dfrac{1}{\sqrt{2}} \right)^{\cos 2x} -(2-\sqrt{2})^{\cos 2x}$. This problem vexes me much because the only way that I could think of to solve this problem would be by substituting $(\sin x)^2=u$, and from there, I...

When I place the trigonometric functions in the "wolfram google", it informs the parity of the function, so, sin(x), sinh(x) -> odd cos(x), cosh(x) -> even tan(x), tanh(x) -> odd cot(x), coth(x) -> odd sec(x), sech(x) -> even csc(x), csch(x) -> odd arcsin(x), arcsinh(x) -> odd...

This is my very first post - so i hope I don't break any rules - its more of a formula rearranging question/confirmation so here goes... Homework Statement Currently working on friction - static/kinetic - so in my textbook it states in a side bar "info bit" that tanθ=sinθ/cosθ my...

Homework Statement [0,1]∫(3x)dx/(4-3x)^1/2 (3xdx divided by square root of 4-3x) Homework Equations The Attempt at a Solution I could not get the bookish answer of that...actually my answer was wholly different... i let 4-3x (without square root) = t and then use substitution...

Hellow! If we can equal the first derivative with a trigonometric function: \frac{dy}{dx}=tan(\theta) So, the second derivative is equal to which trigonometric function? \frac{d^2y}{dx^2}=? Thanks!

Homework Statement please help me with this integration problem? ∫(1/sinx+ cosx) dx Homework Equations i don't know any proper substitution in this question,maybe there are none The Attempt at a Solution i tried rationalizing and it has got me this far...

any hints on how to work out this problems. $\displaystyle\int\frac{dx}{(1-sinx)^2}$ $\displaystyle\int\sin x\sin2x\sin3x dx$ thanks!

Homework Statement d/dx(sec(x)/1+tan(x) Evaluate at x=∏/6 Homework Equations The Attempt at a Solution ((1/cos(x))(1+tan(x))-(sec(x))(sin(x)/cos(x)))/(1+tan(x))^2 ((1/cos(x))-(sec(x))(sin(x)/cos(x)))/(1+tan(x)) I used the quotient rule and reduced what I could. Have I done this...

find the values of other five trig functions $\csc\theta=-2\,and\, \cot\theta>0$ my solution $x=-2$ $y=-1$ $r=\sqrt{5}$ $\displaystyle \sin\theta=-\frac{1}{\sqrt{5}}$ $\displaystyle\cos\theta=-\frac{2}{\sqrt{5}}$ $\displaystyle\cot\theta=2$ $\displaystyle\tan\theta=\frac{1}{2}$...

I will do my best to describe the problem I am working on. The problem is not from a textbook or anything but something I am working on independently to strengthen my first year calculus knowledge. What I did is I took sin(x) and -sin(x) and graphed them together. Sin(x) and -sin(x)...

Hello. I was doing a (simple) physics problem and stumbled with a mathematical problem. I was doing a projectile motions problem and I have set up my equation like this:Δx = Vi (cosθ) (t) 270= 25cosθ t t = 270 / (250cosθ) And this is where I'm having problems. I know from my high school trig...

Okay, so I know how to apply basic trigonometric functions to solve right triangles. However, I am not quite sure how to manipulate trigonometric functions to solve for more complex questions involving non-right triangles, like the question I have attached. I have to use the basic trigonometric...

Trigonometric functions -->sine function EASY! Homework Statement Consider the trigonometric function f(t)=-1+4sin(0.5π(t-1)). (a) What is the amplitude of f(t)? (b) What is the period of f(t)? (c) What are the maximum and minimum values attained by f(t)? Homework Equations...

Hello, I got problem with A homework "find an equation of the tangent line to curve at the given point. $y=sec(x)$. $(pi/3,2)$ progress: $y'=sec(x)tan(x)$. So basicly that sec(x) don't say me much so i rewrite it as $1/cos(x)$ $y'=1/cos(x)•tan(x)$ now i can put $pi/3$ on the function to...

Homework Statement g(x) = 4∏ [cos(3∏x) sin (3∏x)]The Attempt at a Solution g(x) = 4∏ [cos(3∏x) sin (3∏x)]' 4∏{[cos (3∏x)][sin(3∏x)]' + [sin(3∏x)][cos(3∏x)]'} = 4∏{[cos (3∏x)][cos(3∏x) . (3∏)] + [sin(3∏x)][-sin(3∏x) . (3∏)] = Now, my question is: Can I combine the numbers and have the...

Hello, Im currently on chapter about derivate trigonometric functions. It have been hard for me to understand this sec,cot,-csc? Why do you rewrite example $1/cos^2x$ as $sec^2x$? when I get like sec,csc etc i kinda feel i have no clue what it means. Then you think what do Petrus mean? example I...

Find y^{I} (sinxsecx)/1+xtanx The supplied answer is 1/(1+xtanx)^{2} I got stuck with an extra x on top at the end. Where did I mess up at? y^{I}(sinxsecx)/1+xtanx = [1+xtanx*f^{I}(sinxsecx)-sinxsecx*f^{I}(1+xtanx)]/(1+xtanx)^{2} =...

Here is the question: Here is a link to the question: Given 0<x<orequalto 1, determine the value of inversine (x) + inversetan (squareroot(1-x^2)/x)? - Yahoo! Answers I have posted a link there to this topic so the OP may find my response.

I have always capitalised the first letter of my trigonometric functions, for example, writing Sinθ as opposed to the usual sinθ. Is it wrong to capitalise them? Does it make a difference in meaning?

Does ##(\sin^{-1}\theta)^2 =\sin^{-2}\theta## ?

Determine the signs of the trigonometric functions of the angle -200° in standard position. sin(-200°) cos(-200°) tan(-200°) csc(-200°) sec(-200°) cot(-200°) Information: Q1= (All Positive) Q2= (sin csc) Q3= (tan cot) Q4= (cos sec) Answer: sin(-200°) = Positive cos(-200°) =...

Find the values of the six trigonometric functions of an angle θ in standard position whose terminal side is containing the points (-3,0) Sinθ= Cosθ= Tanθ= Cscθ= Secθ= Cotθ= I believe the following are correct But I am not sure, Please give insight Sinθ= 0/3 Cosθ= -3/3 Tanθ= 0/3...

Does anyone know of websites where I can find many problems on the topic in the title line (my textbook has far too few)? Thanks!

Homework Statement A ship is d feet from a dock (horizontal distance). The dock is 40 feet above sea level. The angle of depression from the dock to the ship is θ. Write θ as a function of d. Homework Equations This question is accompanied with choices. The choices are (A) θ = 40arctan(d) (B)...

I tried to solve it but confused. Pls. help me to solve this equation: dy/dx + (e^x)*Sec(y) = Tan(x); (hint: integrating factor is e^-ax, and a is unknown, a ε ℝ, find it, solve the equation) Thnx.

Homework Statement Solve the differential equation: \frac{dy}{dx} = cos^2 (x) cos^2 (2y) The Attempt at a Solution I rewrote the equation \frac{dy}{cos^2 (2y)} = sec^2 (2y) = cos^2 (x) dx. Then I integrated, \frac{tan(2y)}{2} = \frac{1}{2} (x + sin(x)cos(x)) + c. Then I solved for y...

1. Sin^2(x) = 3 – x Answer: 2.97 Attempts: 1-cos^2(x) = 3 – x cos^2(x) - x + 2 = 0 Factored it and got x = pi = 3.14 It’s a multiple choice question, and other answers were 3.02,3.09 which are few decimal places off so the answer must not be pi since it's not even a choice. Is the...

Homework Statement Find the derivative of: sqrt(x^2-4)-2tan^-1{.5*sqrt(x^2-4)} Homework Equations U'/1+U^2 U'=x/2sqrt(x^2-4) 1+U^2=x^2 The Attempt at a Solution I combined the above components but my answer is incorrect. I feel that I might have the wrong answer for...

Hi everyone, Homework Statement My problem is just to derive a simple formula, which is http://www.texify.com/img/%5Cnormalsize%5C%21%28-1%29%5E%7Br%28r%2B1%29/2%7D%20%3D%5Csqrt%7B2%7D%20%5Cmbox%7Bcos%7D%20%5Cfrac%7B%5Cpi%7D%7B4%7D%282r%2B1%29.gif Here r is a positive integer. The Attempt...

Hello, do you have any strategy to suggest in order to solve the following system of partial differential equations in x(s,t) and y(s,t)? \frac{\partial x}{\partial t} = x - \frac{1}{2}\sin(2x) \frac{\partial y}{\partial t} = y \; \sin^2(x) (note that the partial differentiation is always with...

I found this question on a website. Homework Statement Prove that \displaystyle \int_{0}^{\pi}\frac{1-\cos(nx)}{1-\cos(x)} dx=n\pi \ \ , n \in \mathbb{N} 2. The attempt at a solution Here's my attempt using induction: Let P(n) be the statement given by...

Homework Statement [SIZE="7"]∫ (x+2)dx/√(4x-x2) Homework Equations why was the -2 in -2(x-2) was ignored? The Attempt at a Solution so first i let u= 4x-x2 then, du=4-2x = -2(x-2) so to get (x+2) i equate it to (x-2)+4 so ... [SIZE="7"]∫ (x+2)dx/√(4x-x2) =...

I'm self-studying Calculus and would like to ask some doubts about the following question: Homework Statement If, in t seconds, s is the oriented distance of the particle from the origin and v is the velocity of the particle, then a differential equation for harmonic simple motion is...

Homework Statement Hello again, not looking for anyone to solve this problem this time I just need to know what the operation I'm supposed to do is called, so I can go research it and learn it. If sin(t) = -12/13 with 3pi/2 < t < 2pi, find the following: b) cos(t - 11pi/6) Homework...

f(x)= ((cosx)^{2}+1)/e^{x}^{2} So for the limit of f(x) as x→∞ I would just input ∞ for x. I'm confused after this though, wouldn't it just be ∞/∞ = 1? the next part says show that there exists a number c ε (0,1) that f(c)=1 I don't know what this is asking for me to solve.

find the derivatives of differentiation of trigonometric functions 1. y=cos(3x^2+8x-2) 2. y=tan^3 2x 3. y=sin5x sin^5 x 4. y=Square root of 4sin^2x+9cos^2x help here please.. i can't understand trigonometric functions sorry admin or moderator, i just search the net on how...

Homework Statement A skier races down an 18 degree ski slope. During a 5.0s interval, the skier accelerates at 2.5m/s squared. What are the horizontal and vertical components of the skiers acceleration during this time?Homework Equations d = ViT + 1/2aT^2 d=distance Vi=initial velocity...

Hi, For my exams, I am provided with a list of trigonometric functions. I do know at least a good half of those I'm supposed to know but I was wondering if I could get away with *just* knowing how to use them? I know things like sin^2(x)=1 - cos^2(x) or sin(A+B) = sinAcosB + cosAsinB but...

Homework Statement Find the Derivative of: (ln(cos4x)) / 12x^2 Homework Equations y' ln(x) = 1/x The Attempt at a Solution I have determined the correct answer, but I am still confused as to how I came to the solution. Starting with the numerator, the derivative of cos...

I want a timeline for trigonometric function and how it was developed. Just like who created it and stuff like that. Did the greeks know about trigonometric functions? Is a tangent in calculus the same as a tangent in trigonometry and the function os a trigonometry? How do trigonometric...

1. Hi, I have a pre-calculus final tomorrow, and there are a few questions I don't understand. I'd truly appreciate it if you could help :) 1. If sin(theta)=1/4, theta in quadrant II, find the exact value of cos(theta+pi/6) 2. sin(sin^-1(2/3) + cos^-1(1/3)) -- simplify 3...

Dear all, Homework Statement Draw behavior around (0,0) of solutions to the following nonlinear system \left( \begin{array}{c} x'(t) \\ y'(t) \end{array}\right) =\left( \begin{array}{cc} cos {x(t)} + sin {x(t)} + {x(t)}^2 + {x(t)}^2{y(t)}^3 \\ -x(t) + {y(t)}^2 + y(t) + sin {y(t)}...

Homework Statement Find x base of triangle: 2 pieces, 8+12 opposite end: x angle: \Theta ; angle formed by triangle of 8 units and x : 2\Theta Homework Equations tan\Theta = opp/adj tan 2\Theta = 2tan/1-tan2 The Attempt at a Solution tan\Theta= x/20 tan 2\Theta = x/8...

Homework Statement Prove: lim (n→0) {(sin n cos n) / (ⁿ√(1 - tan² 2n + tan⁴ 2n - tan⁶ 2n + ...))} = 1Homework Equations The Attempt at a Solution The denominator is an infinite geometric series, using the sum formula of an infinite geometric series, I simplify the limit: lim (n→0) {(sin n cos...

Hi, everyone, I am mathstkk, I am new to the Physics Forum, but I think, at my first sense, this forum is going to be helpful to me^^ Recently, I met one problem about matrix. The problem is as follow: Show that the matrix below has NO non-trivial solution if a+b+c=0 The matrix is 1...

Homework Statement 1) lim sin^2(3x)/x^2 x->0 2) lim 2sin5x/(3x-2tan2x) x->0 Homework Equations lim sinx/x = 1 x->0lim tanx/x = 1 x->0 The Attempt at a Solution We just began working with limits, and we haven't covered much of trig functions at all, but our prof gave us...