Trigonometric Definition and 1000 Threads

hi every one, i have one doubt i studied abt trignomentry. there finding the triangle angle or side of the triangle using sine function. if we are taking right angle triangle sine A = opp/hypo, cos A = adj/hypo and tan A=opp/adj. here we are finding angle for A only why we are having three...

Homework Statement Prove (using the left side): sinΘ tanΘ = cosΘ sec^2Θ - cosΘ Homework Equations The Attempt at a Solution

I received the following email: I can't see the logic in assuming (for example) that a function containing sqrt (a^2 - x^2) in the integrand would lead you to substitute x with a trig reference. Why a trig reference? What connection does the integrand, trig-less function have to trigonometry...

I'm stuck on a question from my calculus homework...T_T Here's the question... There is a large clock at the front of the lounge on the paddle steamer. The hour hand is 28 cm long and takes 12 hours to rotate once. At 2 o'clock the tip of the hour hand is 195 cm above the floor. There's...

Homework Statement So, for absolutely no good reason I decided to practice trigonometric substitution. I started with \int \left(1-x^2\right)^{-1/2} dx, and that was easy, everything canceled out nicely. Then I tried \int \left(1+x^2\right)^{-1/2} dx, and although the integral was fine...

Given sinθ = 0.6, calculate tanθ without using the inverse sine function, but instead by using one or more trigonometric identities. You will find two possible values. I found one of the values using sin^2 (theta) + cos^2 (theta) = 1 I tried using cos (90 + theta)= sin theta to find the...

Homework Statement ∫dθ/(1+βcosθ)^2 ; -1<β<1 θ=0 to 2pi Homework Equations The Attempt at a Solution attempt solution: 1) make substitution: dθ=dz/iz Z=e^iθ cosθ=1/2(Z+1/z) 2) substitute: 1/i*dz/(β+Z(1+(β^2)/2)+((3βZ^2)/2)+((β^2)Z^3)/4)+((β^2))/4Z) 3) Next ...

Homework Statement integral 31(cos^2x)(sin(2x)dx Homework Equations The Attempt at a Solution I am so lost on this problem... Any suggestions would be great

Homework Statement Solve for x for 0\leq x\leq 2 \pi in the following equation: sin x tan x + tan x - 2sinx + cos x =0 Homework Equations N/A The Attempt at a SolutionI tried making tan x = \frac{cos x}{sin x}, but did not have any luck, and am very confused on how to solve the equation. I...

This problem looks relatively simple, but the coefficient in front of the variable is causing issues: \int{\sqrt{1-4x^{2}}}dx So I started like this: x=sin(\theta) dx=cos(\theta)d\theta \int{\sqrt{1-4sin^{2}(\theta)}cos(\theta)d\theta} Normally you can remove the constant from the root and...

Homework Statement integral of secxtanx/secx -1 Homework Equations sec u du = ln |sec u +t an u | + c The Attempt at a Solution sec u +tan u | + c

Limits of Trigonometric Functions. URGENT! Homework Statement Evaluate stackrel{lim}{x \rightarrow0}[/tex] [sin(\frac{2e}{x3}) \bullet (arctanx)] Homework Equations All I know is that the equation stackrel{lim}{x \rightarrow0}[/tex] \frac{sin x}{x} = 1 might be helpful, but I'm not sure...

Homework Statement Derive the following: y = (cosxsin2x)-2 2. The attempt at a solution Basically I saw this as a power rule with two products in the middle. So y = -2 (cos2cos2x-sinxsin2x)-1 But the correct answer is completely different, it's: 4(3sin2x - 1) all over...

Homework Statement There are infinitely many points on the curve y = \frac{sin x}{\sqrt{2}- cos x} at which the tangent line to this curve is horizontal. Find the x- and y-coordinates of one such point. Homework Equations y' = slope of the tangent line Etc., etc. The Attempt at a...

Hi, Does anyone know of an analytic solution for the integral \int_{0}^{\pi}\sin\theta\exp\left(a\sin^{2}\theta+b\sin\theta\right)d\theta Thanks.

This is related to my previous https://www.physicsforums.com/showthread.php?t=398964". I am having trouble to get the maximum of the following trigonometric function: \cos^m\theta_1(c\cos^n\theta_2+s\sin^n\theta_2)+\sin^m\theta_1 ( c\sin^n\theta_2+s\cos^n\theta_2)...

Hello, Could you please clarify if this is correct: If tan^(-1)(x) = Pi/2 - tan^(-1)(1/x) Then if we have (ax) as the angle where a is a constant, do we get: tan^(-1)(ax) = Pi/2 - tan^(-1)(a/x) or does the constant go on the bottom with the x? i.e. or: tan^(-1)(ax) = Pi/2 -...

Homework Statement Evaluate \int\frac{e^t}{\sqrt{e^2^t+9}} Homework Equations N/A The Attempt at a Solution i'm using substitution tan \theta = \frac{e^t}{3} or i also can use tan \theta = \frac{3}{e^t} both will get the same answer. am i right? because my...

Homework Statement \cos (2 \theta)=- \cos ( \theta) Homework Equations The Attempt at a Solution In general \theta = 2n \pi +/- \alpha \mbox{ where } \cos \theta = \cos \alpha Because \cos(2 \theta) = - \cos( \theta) \mbox{ then, } 2 \theta = 2n \pi -/+ \theta taking 2...

Homework Statement This problem is solved in my book however I don't totally understand it. find the integral of sin^2 (x) Homework Equations [b]3. The Attempt at a Solution [/ the integral of sin^2 (x) = integral of (1-cos2x)/2 dx = (1/2)x -(1/4)sin2x + C I don't...

Homework Statement Find the constants A and B such that the function y = Asinx + Bcosx satisfies the differential equation y'' + y' - 2y = sinx Homework Equations None The Attempt at a Solution My attempt: y = Asin x + Bcosx y' = Acosx - Bsinx y'' = - Asin x - Bcosx y''...

This is part of the identity proving question . from \sin C=\frac{2}{\sqrt{29}} , how can i reach C=\frac{1}{2}\sin^{-1} (\frac{20}{29}) ?

Hi, can you help me solve these three questions? Please show each step. Thanks. 1. solve for x: arcsin(6x-pi)=1/8 2. Find an equation of the tangent line to the graph of y = arcsin (6x) at the point ((1/(6sqrt2),(pi/4)) 3. Find the indefinite integral of 1/sqrt(81-100x^2)

Homework Statement 1. Given cos α = -24/25 in Quadrant II and sin β = -5/13 in Quadrant III, find sin (α + β). 2. Given sin α = 4/5 in Quadrant I and cos β = -12/13 in Quadrant II, find cos (α + β). Homework Equations I don't even know where to start! The textbook doesn't list any...

Homework Statement cos(x)+2tg(x) = 7/(4*cosx(x)) Solve for x on the real numbers set. Homework Equations tg(x) = sin(x)/cos(x) , cos^2(x) = 1-2*sin^2(x) , The determinant is D = b^2 - 4ac , Also cos(x) ,tg(x), sin(x) | -1 < x < 1 The Attempt at a Solution For final arrangement I...

Homework Statement \int{\frac{x^{3}}{\sqrt{4 - x^{2}}}} NOTE: The use of "0" is theta. I couldn't figure out how to insert one :\ Homework Equations The trig identity sin^{2}0 = 1 - cos^{2}0. The Attempt at a Solution I thought I completed the problem fine, but I realized WolframAlpha has a...

The angle of elevation from the top of a house to a jet flying 2 miles above the house is x radians. If d represents the horizontal distance, in miles, of the jet from the house, express d in terms of a trigonometric function of x. The graph the function for 0< x <pi.

\int\frac{x}{\sqrt{x^2+x+1}}dx \int \frac{x}{\sqrt{(x+\frac{1}{2})^2+\frac{3}{4}}}dx u=x+\frac{1}{2} \int \frac{u-\frac{1}{2}}{\sqrt{u^2+\frac{3}{4}}}du u=\frac{\sqrt{3}}{2}tanT du=\frac{\sqrt{3}}{2}sec^2TdT \int...

Hi. I'm having troubles calculating this indefinite integral. I have tried a few things, but none seem to work. Actually, universal substitution does make it possible to integrate, but there has to be some shorter, more elegant way. Anyone?

9x^2-4y^2=36 \frac{x^2}{4}-\frac{y^2}{9}=1 y=\frac{3}{2}\sqrt{x^2-4} 3\int_{2}^{3}\sqrt{x^2-4}dx x=2sect dx=2secttant 12\int_{a}^{b}tan^2tsectdt 12\int_{a}^{b}(sec^2t-1)(sect)dt 12\int sec^3tdt-12\int sectdt 6\int secttant-6\int ln|sect+tant|...

Homework Statement Integrate at interval [0,T] (T and k are given real numbers) the 2. Relevant equation _{0}^{T}\int \frac{sin(p)}{\sqrt{k+p}}\ dp The Attempt at a Solution \ Using\ substitution\ u\ =\ tan(p/2),\ results\ as\ :\ p\ =\ 2*arctan(u)\ \ ;\ \ dp\ =\...

Homework Statement \int\frac{1}{t^3\sqrt{t^2-1}}dt with limits of integration [\sqrt{2}, 2] Homework Equations The Attempt at a Solution Using trig. sub, I have sec \theta=t dt=sec \theta tan \theta d \theta \int\frac{1}{t^3\sqrt{t^2-1}}dt with limits of integration...

Homework Statement I'm in an Intermediate Mechanics course right now, and while the Physics itself isn't giving me too much trouble, I am lagging behind in the Math department. I am trying to solve the integral: \int cos(\omega t) sin(\omega t - \delta) dt Homework Equations...

Homework Statement prove that: tan(1+cos(x))^2 = 1-cos(x) Homework Equations trig identities, like the pythagorean, sum/difference, double/half angle identities, power reducing identities, etc... The Attempt at a Solution i'm not sure where to start; i tried using the pythagorean...

sin|x + y| = ? cos|x + y| = ? Is there any formula for these?

cosh x= e^x+e^-x/2 sinh x= e^x-e^-x/2 Can someone explain why the hyperbolic trigonometric functions are defined in terms of the natural exponential function, e^x ?

Homework Statement Cos^2x-Sin^2x/2 SinxCosx The Attempt at a Solution I changed cos^2x to 1- sin^2x which then the equation was 1- s sin^2x/2snxcosx and i have no idea how to make this a single trig. function

Homework Statement Without using tables(calculators) find the numerical value of Sin[Pi/8]^2 - Cos[3 (Pi/8)]^4 Homework Equations The Attempt at a Solution I tried changing it to: 1-cos[pi/8]^2 - cos[3pi/8]^4 but have no idea where to go... its really got me scratching my...

Homework Statement 3sinx = 1 + cos 2x Homework Equations N/A The Attempt at a Solution 3sinx = 1+1 - 2sin2x (Trigonometric Identity) 3sinx = 2-2sin2x 2sin2x + 3sinx = 2 I do not know where to go from there. My book tells me the answer is 30o and 150o

Homework Statement Let R be the smaller of the two regions enclosed by the elipse 144 x2+64 y2=9216 and the line $ x=(8 \sqrt{2})/2$. Find the area of the region R. Homework Equations The Attempt at a Solution my textbook doesn't have anything like this.. i have no idea where...

Hi I've got this problem which has really been bothering me. How are you supposed to prove that: (Sin[A] Sin[2 A] + Sin[3 A] Sin[6 A])/(Sin[A] Cos[2 A] + Sin[3 A] Cos[6 A]) is identicle to tan[5A]. I am almost sure that I've got to use the factor formulae, but I've had no luck. Maybe...

Homework Statement $\int \frac{\sqrt{1-4x^2}dx}{x}$ Homework Equations The Attempt at a Solution im stuck and i have no idea why I am getting the wrong answer. let 2x = sin\phi dx = cos\phi d\phi / 2 $\int \frac{\sqrt{1-(2x)^2}dx}{x}$=$\int...

Homework Statement Let R be the region enclosed by the curves y=6sin2x and y=6 over the segment [ π/2,3π/2]. Find the volume of the solid that is obtained by rotating R about the line y=−1.1. Homework Equations $\displaystyle \Large pi * \int _a^c x((r+yt)^2 - (r+yb)^2)dx$...

I met the following expression in a QM book: \frac{sin[(n+1/2)\pi+\epsilon]}{cos[(n+1/2)\pi+\epsilon]}=\frac{(-1)^n\cos(\epsilon)}{(-1)^{n+1}\sin(\epsilon)} where \epsilon << 1 No matter how hard I try (sine of sum, etc.), I can't see the intermediate steps to this result...

So the orginial question asked what angle to fire a gun to hit a moving target, and i got all the way to 40sinθcosθ-10sinθ-1 = 0, but we aren't supposed to use calculators so how would you solve this by hand. Thanks!

Homework Statement Solve for x. x is greater than or equal to 0 and x is less than or equal to 2pi. (4/3)sinxcosx-sin22x=0 If there is a better way to approach this question than the way I did it below, please post it. Thanks.Homework Equations N/A The Attempt at a Solution...

Homework Statement how to show using MVT that cos(cos x) is a contraction. Homework Equations | d/dx (cos(cos x)) | = | sin(cos x) sin(x) | < sin 1 < 1 The Attempt at a Solution Using that relation, the original problem is easily solved. My question is, how do we know: |...

Im trying to find lim (2x+cos x)/x as x --> inf. I've started out by multiplying with the conjugate. [(2x+cos x)(2x-cos x)] / x(2x-cos x) = =(4x2-cos2x)/(2x2-x cos x) But now I'm lost - any hints?

Homework Statement The original problem is this: ab^2*cos(2x)*(cos(x))^2 + ba^2*sin(2x)*(sin(x))^2 = 0 And some of the more "logical" forms I've got to are these:2[tan(x)]^3-2tan(x) = -b/a tan(2x)*(tan(x))^2=-b/a But I can't solve these equations so I'd like to ask for some help here.

Hi, I would like som help on this one: Give all the real soulutions to the equation \frac{7}{4}-2sin(x) - cos^2(x) = 0 i tried the common identities, like replacing cos^2(x) with 1-sin^2(x) any ideas?