Trig Definition and 1000 Threads

Homework Statement ∫√(4-x^2)/x dx Homework Equations The Attempt at a Solution a^2=4 u^2=x^2 ⇒ u=asinθ a=2 u=x x=2sinθ sinθ=x/2 (Our professor uses a triangle method which I won't draw) 2cosθ=√(4-x^2) dx=2cosθ dθ ∫√(4-x^2)/x dx=∫2cosθ/2sinθ dθ...

Homework Statement prove that Acosx+Bsinx=sqrt(A^2+B^2)sin(x+alpha) where tan(alpha)=A/B The Attempt at a Solution none so far except that sin(x+alpha)=sinx cos(alpha)+cosx sin(alpha) Any help is appreciated. This is due tomorrow (It was just assigned yesterday). I've taken a year...

just wondering if i can still do this, attempted the following: ʃʃ cos(x+y)dxdy with upper limits of pi/2 and lower limits of 0 for both integrals My answer came out as 0. Can anyone confirm this?

Hi there need help understanding trig ratios thanks a lot vati

Hello. Up until this point I have been solving this numerically, by propagating the state vectors and checking for a collision, however that is inefficient, so I would like an analytic solution. Given lengths r, and d, as well as angle t, is there a way to find length s?

A fully loaded Cessna-182 airplane of mass 1260 kg has an engine failure when flying with an airspeed of 126 km/h at an altitude of 2870 m on a calm day. It then glides at a constant glide angle (which is the direction of flight below the horizontal) towards a safe landing at this constant speed...

I had some questions on a test and i got these two wrong.. x is greater than or equal to 0 and x is less than or equal to 360 1) 2sin x + sin x cos x = 0 2) sin 2x = -1/sqrt(2)

Homework Statement I'm given the problem: \int\frac{\sqrt{y^{2}-25}}{y} dy Homework Equations I set y = 5sec(u), and solve for the subsitution. The Attempt at a Solution At the culmination of my solution, I achieve: 5tan(u) - 5u + C Here is my dilemma, u stands for...

Homework Statement Even if you have no idea what on Earth any of this stuff is but have a vast knowledge in complex number system you might be able to help me as this is what I believe is preventing me from making sense of this stuff... Ok I'm trying to understand how you would know that...

Can anyone help me with these two limit problems... solve: lim h->o (h^2-h+sinh)/2h and lim y->0 (sin3cot5y)/ycot4y I know lim x->0 sinx/x=1, but I can't figure out how to get these two into that format.

Homework Statement Well this is technically from a calculus problem but my question focuses only on the trig of the problem so I am posting it here. This is for graphing second degree equations with a nonzero xy Homework Equations Given: Ax^{2}+Bxy+Cy^{2}+Dx+Ey+F=0 where B \neq...

Homework Statement I don't know how to solve these. How do you evaluate the integral of \frac{3dx}{\sqrt{3+X^2}}? I know you have to set x=atan\theta. our a is \sqrt{3} so x =\sqrt{3}tan\theta. That means dx=\sqrt{3}sec2\thetad\theta. I also made a right triangle using the information...

Homework Statement I need help evaluating the integral Cotx3/10 I factored out the 1/10 from the integral and am just left with (1/10)*Cotx3 from here i do not really know what to do. I rewrote it in terms of sine and cosine to get (1/10)*(Cosx3/Sinx3)dx I multiply the integral...

I have this question in my trig/pre cal class and I have no idea how to approach it what so ever. In 1893, George Ferris engineered the Ferris Wheel. It was 250 feet in diameter. If the wheel makes 1 revolution every 50 seconds, then h(t) = 125sin (pi/25t - pi/2) + 125 represents the...

Homework Statement the problem is INTEGRAL 6dz/(z^2(sqrt(z^2+9)) z^2+ a^2 , then z=a*tan@ where a here is 3, because 3^2=9 , i use @ here to represent theta substituting this for z; Int[6/(z^2(sqrt(z^2+9))]dz= Int[(6*3sec^2@d@)/(9tan^2@(sqrt(9tan^2@+9))]=...

Homework Statement sin^3(x)-cos^3(x) sin(x) - cos(x) equals 1 + sin(x) + cos(x) Homework Equations Not sure :/ The Attempt at a Solution Not sure where to even start.

Find the inverse of the rotation matrix cos(theta) -sin(theta) sin(theta) cos(theta) I have no problems finding the inverse of a standard 2x2 matrix, however I am confused by the trig functions. I guess the determanent would be 2cos(theta) and I would end up with...

Homework Statement sin(tan-1(x)) Homework Equations The Attempt at a Solution y=tan-1(x) tan(y)=x sec2(y)= 1+tan2(y) sec(y)=\sqrt{1+x^2} This is where I'm getting stuck. I know that I have to say that the sin(y)= whatever, but I'm not sure how to tie the sin sec and tan...

"simple" trig problem Homework Statement 2(sinA+cosB)sinB=3-cosB. Find 3tan2A+4tan2B Homework Equations Trig Identities The Attempt at a Solution well, i expanded 3tan2A+4tan2B= 3sin2Acos2B+4sin2Bcos2A all over cos2Acos2B after that I am stuck.

Homework Statement What is the integral of tan x sec2x with respect to x? Homework Equations The Attempt at a Solution I have no idea as to how I should proceed!

Homework Statement I am working on some calculus homework and I am stumped by this question. It is in the section "derivatives of trigonometric functions." It seems like it should be easy, but I can't think of where to start. I don't need any answers and you don't need to present any...

Homework Statement Write the Trigonometric Expression as an algebraic expression. cos(2arccos 2x) Homework Equations Probably the inverse properties, I'm not sure. The Attempt at a Solution I know I can rewrite this equation as. u= arccos 2x cos(2cos u=2x) I can also...

Homework Statement (Cos[x]^2) (Tan[x] + Cot[x]) Simplify the equation by hand! Homework Equations The Attempt at a Solution cos^2 / (tan + cot) cos^2 / (sin/cos + cos/sin) * sin*cos/(sin*cos) sin*cos^3 / (sin^2 + cos^2) sin*cos^3 / 1 sin(x) * cos^3(x) this is wrong b/c i divided it... NVM...

Homework Statement tan((π(x))/2) = √(3)/2 Homework Equations The Attempt at a Solution tan(x) = √(3)/2 x= π/6 + πn, since Tan has a period of π This is where I'm stuck

Homework Statement [PLAIN]http://img708.imageshack.us/img708/1344/trig.jpg The angle c is separated from a 2d plane by angle b (perpendicular to the 2d plane). Angle a is angle c projected onto the 2d plane. What is a in terms of b and c? Homework Equations The Attempt at a...

Homework Statement lim x appraoches 0 sin(x)/(x+tan(x)) Homework Equations I have tryed everthing. Can someone show me how to do this. The Attempt at a Solution

Just wondering how this is simplified to the third line: If w, z are complex numbers wz = rs( cos\alpha + isin \alpha ) (cos \varphi + isin \varphi) wz = rs(cos\alpha cos \varphi - sin \alphasin\varphi) + i(sin \alphacos\varphi + cos \alpha sin \varphi)) wz = rs(cos (\alpha...

Hi Given this limit \lim_{h \to 0} \frac{1-cos(h)}{h} = 0 can you rearrange (sin(x) (\frac{cos(h)-1}{h})) to (sin(x) \cdot -1 \cdot (\frac{1-cos(h)}{h})) so that when you take the limit as h goes to 0 you get: sin(x) x -1 x 0 = 0 thanks

Homework Statement Find all solutions for 6sin2x-5sinx+1=0 over the interval [0, 2pi[The Attempt at a Solution 6sin2x-5sinx+1 (-3sin+1)(-2sin+1) 1/3 and 1/2 On unit circle, 1/2 is equal to pi/6 and 5pi/6... Not sure how to figure out 1/3! Any help would be much appreciated!

Homework Statement The base of an isosceles triangle is 20 cm and the altitude is increasing at the rate of 1 cm/min. At what rate is the base angle increasing when the area is 100 cm^2?Homework Equations The Attempt at a Solution Im very unsure about my solution method. I have attached a...

Homework Statement Find \int(x+2)dx/sqrt(3+2x-x2) Homework Equations \intdu/sqrt(a2 - u2) = sin-1u/aThe Attempt at a Solution I began by completing the square: 3+2x-x2 = 4 -(x2-2x+1) So, 4-(x-1)2 = a2-u2 and a=2 and u=(x-1) Further, since x=(u+1), dx=du and (x+2)=(u+3) Substituting, I...

Homework Statement If pi ≤ Θ ≤ 2pi and cos Θ = cos 1, what is the value of Θ? Round to nearest hundredth. Homework Equations The Attempt at a Solution cos 1 = ~.54 then I didn't really understand how to interpret the "If pi ≤ Θ ≤ 2pi" Thanks for your help.

Homework Statement Hi, I need to find the spectrum of the following function: i=I_0[e^{\frac{-0.01(cos(2\pi 1000t)+cos(2\pi 100000t))}{0.026}}-1]Homework Equations the Fourier Transform would be: \int_{-\infty }^{\infty }I_0[e^{\frac{-0.01(cos(2\pi 1000t)+cos(2\pi...

Homework Statement integrate tan(x)sec^4(x) dx Homework Equations The Attempt at a Solution int tan(x)sec^4(x) dx = int tan(x)sec^2(x)sec^2(x) dx = int tan(x)sec^2(x) (tan^2(x)+1) dx let u = tanx ==> du = sec^2(x) dx = int usec^2(x) (u^2 + 1) /sec^2(x) du = int u(u^2+1)...

[b]1. How do I prove sinxcosxsec^2x=tanx Homework Equations sec^2x = tan^2x + 1 The Attempt at a Solution sinxcosx(tan^2x + 1) tan^2xsinxcosx +sinxcosx sin^2x/cos^2x*sinxcosx + sinxcosx - is this valid? I'm not sure what I've done is even correct - but it doesn't seem...

integral of x/(x2+2x+2)dx first thing i did was complete the square to get x/((x+1)2+1 i tried then having x+1 = tanx but that didnt work out because of the x on top i can't just set w = x+1 what would the right substitution be? any hints or help would be appreciated

Homework Statement I did the question with help, but did not understand why did we multiply e^-i(x/2) How do I know what to multiply for getting the real part of a complex number in exponential form? Homework Equations The Attempt at a Solution

Hello all, excited to be on the forums. I'm having trouble solving a problem from one of my past exams (prepping for final). Could you please guide me? The displacement associated with a wave on a string has the functional form y = 0.2 cos (10x - 4t). What is the wave speed? The answer...

Homework Statement Find the magnitude of a and the smallest positive angle theta from the positive x-axis to the vector OP that corrosponds to a. a= (3,-3) Homework Equations a1 = ||a|| * cos theta a2 = ||a|| * sin theta 3. The Attempt at a Solution ||a|| = \sqrt{}(9+9) =...

Homework Statement Differentiate e^x * cotx / 5sqrtx^2 [Sorry for not using the formatting things. They didn't seem to be working for me, and this is urgent!] Homework Equations The quotient rule seems like that's the way to go... The Attempt at a Solution At first I tried using...

Homework Statement A football kicker can give the ball an initial speed of 25 m/s. What are the least and greatest elevation angles at which he can kick the ball to score a field goal from a point 50 m in front of goalposts whose horizontal bar is 3.44 m above the ground?The Attempt at a...

Homework Statement Find the critical numbers of the function: f(θ) = 2cosθ + sin^(2) θ Homework Equations None The Attempt at a Solution I differentiated the equation and got -2sinθ(1 - cosθ) and found the critical values to be θ = 0 degrees + 2pie * n but the correct answer...

I know that \sin^2 b= (\sin b)^2 and in general \sin^n b=(\sin b)^n if n is a positive integer . What if n is a negative integer , would it be \sin^{-1}b=(\sin b)^{-1}=\frac{1}{\sin b} I don't think this is right , because properties of indices only works for numbers and NOT function...

I am absolutely stoned by this equation. I've looked through all the trig identities and the only one that comes close to be used in here is sin2u = 2sin(u)cos(u), but there is that lamba... Any suggestions?

Homework Statement 1/cscx-sinx = secx tanx Homework Equations cscx = 1/sinx secx = 1/cosx The Attempt at a Solution 1/cscx-sinx = secx tanx L.S. = 1/cscx-sinx = 1/(1/sinx)-sinx R.S. = secx tanx = (1/cosx)(sinx/cosx) This is where I'm getting confused. Why can't...

Homework Statement Find dy/dx, given y = sin( 3 x ) cos( 6 x ) Homework Equations product rule= f'g+g'f The Attempt at a Solution I used the product rule and got this, but its supposedly wrong, what have i done wrong?((3*cos(x))*(6*cos(x)))+((6*sin(-x))*(3*sin(x)))

Homework Statement Cell phone tower #1 has a broadcast radius of 50 miles. Tower #2 has a broadcast radius of 60 miles and is located at a bearing of N 64 W of tower #1. The towers are 100 miles apart the questions: A.How much area has coverage by both towers? (dont need the N 64 W) B.A...

Hi. I'm having trouble trying to understand the relationship between inverse trig functions, especially arcsin x, and pythagorean identity. I know that because cosx=sqrt(1-(sinx)^2), derivative of arcsin x is 1/(cos(arcsin x)) = 1/(sqrt(1-(sinx)^2)arcsinx)) = 1/(sqrt(1-x^2). But how does...

Homework Statement Sin(x)+sin(2x)+sin(x)*Cos(2x)+sin(2x)*cos(x)=0 Solve for all angles x.Homework Equations Sin(2x)= 2sin(x)*cos(x) The Attempt at a Solution Not really sure what to do. I noticed that i could maybe factor out Sin(x), but i do not really know if that is right. I seem to be...

Homework Statement How to get from \sqrt{2+2cosx} to 2cos(x/2) The Attempt at a Solution I'm pretty much stuck on this. I can only see that is simplifies by taking out the common factor 2, which isn't correct.