Trig Definition and 1000 Threads

Homework Statement Given a triangle ABC prove that c sin \frac{A-B}{2} = (a-b)cos \frac{C}{2} Homework EquationsThe Attempt at a Solution It looks rather similar to a formula mentioned in my book's lead-in to this exercise: \frac{a-b}{a+b}=tan\frac{A-B}{2}tan\frac{C}{2} Which can be...

Hi Team... Hope you can help me as I'm sooo confused right now. I've only been doing Math for about 4 months :( Any direction as to how to start solving this problem would be amazing...Fire Rescues Fire trucks with extension ladders are used regularly to remove people from burning buildings...

Homework Statement Find d^2/dx^2 and both complex number forms for the complex number equation (1+icos(x))/(1-icos(y))[/B] Homework Equations 1. z=a+bi 2. re^itheta The Attempt at a Solution I have multiplied both sides by 1+icosy and gotten as far as (1+icosx+icosy-cosxcosy)/(1+cos^2y) but...

Homework Statement Calculate (A×B)⋅C for the three vectors A with magnitude A = 5.00 and angle θA = 25.1∘ measured in the sense from the +x - axis toward the +y - axis, B with B = 4.18 and θB = 62.0∘, and C with magnitude C = 5.82 and in the +z - direction. Vectors A and B are in the xy-plane...

1. The problem statement, all variables and given/known Find the length of the curve $$y=ln(x),\frac{1}{2}<=x<=2$$ Homework Equations Using hyperbolic trig isn't necessary, but it's how my text (Serge Lang's A First Course in Calculus) approaches most square roots, and as a result, it's what...

$$\int_{0}^{\pi/2}\d{}{x} \left(\sin\left({\frac{x}{2}}\right)\cos\left({\frac{x}{3}}\right)\right)\,dx$$ the ans the TI gave me was $\frac{\sqrt{6}}{4}$ the derivative can by found by the product rule. but really expands the problem so not sure how the $\frac{d}{dx}$ played in this.

Homework Statement http://education.Alberta.ca/media/9451970/07_math30-1_released_2014-15.pdf question #7 Homework Equations a=theta*r The Attempt at a Solution I did a=(5pi/6)*20 but the answer is not A

Hello, all. For homework, we got a problem that reads as follows: A Ferris wheel 50 ft in diameter makes one revolution every 40 sec. If the center of the wheel is 30 ft above the ground, how long after reaching the low point is a rider 50 ft above the ground? Our teacher said to model the...

I simplified a trig equation to \theta=\Big\{sin^{-1}(\frac{1}{2})+2\pi k\Big\}\; and \; \Big\{\pi-sin^{-1}(\frac{1}{2})+2\pi k\Big\} Whereas the book simplified it to \theta=\pm\frac{\pi}{6}+\pi k Obviously these answers encompass the same set of values, with the book's answer being much...

Find a formula for g(x)= sin(arccos(4x-1)) without using any trigonometric functions. I have the answer key right in front of me, but i still get how to start it off or the steps in solving these kind of questions or how to do it at all :/ Thanks!

Homework Statement \int\frac{{\rm{d}}x}{1+2\sin^2 (x)} Homework EquationsThe Attempt at a Solution it's some sort of a derivative of arctan, however, when I try to substitute y = \sqrt{2}\sin(x),\ {\rm{d}}y = \sqrt{2}\cos(x){\rm{d}}x I get nowhere with it, atleast I think, since there is a...

Homework Statement f(x)=20+25*sin(0.85x) x = number of hours from start. f(x) = temperature. For how long is the temperature negative (under 0) during the first 10 hours? We haven't learned how to derive/integrate trig equations so that is out of the question. Homework EquationsThe Attempt at...

Homework Statement A ships captain wishes to sail his ship north -east. A current is moving his ship with a velocity of 5.0km/h . If the ship has a maximum speed of 30 km/h what is the ships required heading? Homework Equations Cos angle=A/H The Attempt at a Solution Heading=cosine (5/30)...

I just have a few questions. When using a trig substitution does it have to be under a radical ? eg, suppose I wanted to integrate (x2)/(x2-9), I used a trig substitution of x = 3sec(t) and got the wrong answer and so apparently I had to use partial fractions

Hi, i was just wondering since cosx=1-(x^2/2) is there a similar formatted formula for sinx?? much appreciated :) :)

I know if we set x = \cosh \theta , y = \sinh \theta and graph for all \theta 's, we get a hyperbolic curve since then x^2 - y^2 = 1. But — unlike the case of making a circle by setting x = \cos \theta , y = \sin \theta and graphing all the \theta 's — in the hyperbolic graph the angle...

An airplane starts from a station and rises at an angle of 10 deg with the horizontal. By how many feet will it clear a vertical wall 100 ft. High and 900 ft from the station? I don't get it. Can you provide an image that represent the situation in the problem. Thanks.

Homework Statement Find the 4 critical points f(x,y) = 5ycos(9x) closest to (0,0) Homework EquationsThe Attempt at a Solution fx = -45ysin(9x) fy = 5cos(9x) fxx = -45*9ycos(9x) fyy = 0 fxy = -45sin(9x) y=0 x=pi/18 (0,pi/18) (0,pi/18 + pi/2) (0,pi/18 - pi/2) (0,pi/18 + 3pi/2) Was not...

Determine whether the given differential equation is exact and if so solve it. $$(\tan{x}-\sin{x}\sin{y}) dx+\cos{x}\cos{y} dy=0$$ I got \cos{x}\sin{y}+\sec^2{x}=c but the answer key has -ln|\cos{x}|+\cos{x}\sin{y}=c where did $$ln$$ come from?

Homework Statement A projectile is fired with speed v_0 (velocity subscript zero) at an angle θ from the horizontal as shown in the figure Consider your advice to an artillery officer who has the following problem. From his current position, he must shoot over a hill of height H at a target...

I can't quite work out this derivation I ran into which is essentially...Asin^2(wt) + Bcos^2(wt) = A = B. Is this correct? I know that sin^2(wt) + cos^2(wt) = 1, but I can't reason out how the factoring works here? Any help?

from 0 to π/2 ∫sin5θ cos5θ dθ I have been trying to solve the above for quite some time now yet can't see what I am doing wrong. I break it down using double angle formulas into: ∫ 1/25 sin5(2θ) dθ 1/32 ∫sin4(2θ) * sin(2θ) dθ 1/32 ∫(1-cos2(2θ))2 * sin(2θ) dθ With this I can make u = cos(2θ)...

Homework Statement An airplane is ascending at an angle of 10 degrees is detected 2000m directly above an observer after 20 seconds the angle of elevation to the plane is 48 degrees. How fast is the plane going?Homework Equations The Attempt at a Solution I just don't know what to do next, I've...

Homework Statement Integrate: (sin(2x))^3(cos2x)^2dx Homework Equations Using substitution Cos2x= (1-(sinx)^2) The Attempt at a Solution I sub u= sin2x But then got nowhere because I had cos2x to the power of 2 and I don't know how to compensate for it with du. [/B]

Hey guys, I've been trying to wrap my mind around this problem but I've really come up short. Any help would be amazing. If tanX=10 Find the exact value of cot(pi/2 - x)

Mod note: Moved from technical math section[/color] ∫(2x+6)/sqrt(5-4x-x^2) I have 2/3(ln|tan(theta)+sec(theta)|-3|cos(theta)|) where x=sin^-1((x+2)/3)

Homework Statement I'm doing a statics problem and am following how the solutions manual does it but they skipped a few steps and I'm lost as a result. I have two equations and two unknowns: F and θ (degrees) Homework Equations Equation 1: F*cos(25+θ) = -54.684 Equation 2: F*sin(25+θ) =...

I have probably put around two hours into this question to no avail! 6sin2(x) - 3sin2(2x) + cos2(x)=0 I have too many fruitless attempts to bother typing them all out.. But my instincts at first told me that this looks like a quadratic equation. I have tried using the double angle...

is there an equivalent identity for $\sin^2\omega t?$ please tell me.REGARDS!

1. Homework Statement I need to find the times when the velocity is 0. I am having difficulties finding multiple values for t. v(t)=0 2. Homework Equations v(t)=-40/3*cos(3/2*t)-5.129 3. The Attempt at a Solution Attempt at solution: v(t)=-40/3*cos(3/2*t)-5.129 V(t)=0...

Hello, Preparing for a test, I've had to go through some very basic trigonometry and I've got to thinking why reference angles "work". I've gone through my study material and through another trigonometry book I have around the house and references angles are never proven, the theorem is just...

Homework Statement A and B are two unit vectors in the x-y plane. A = <cos(a), sin(a)> B = <cos(b), sin(b)> I need to derive the trig identity: sin(a-b) = sin(a) cos(b) - sin(b) cos (a) I'm told to do it using the properties of the cross product A x B Homework Equations A x B =...

Homework Statement lim x->0 (2sinxcosx)/ (2x^2 + x ) Homework Equations 2sinxcosx = sin(2x) The Attempt at a Solution denom. factors to x(2x +1) how to proceed?

Homework Statement Find the equation of the asymptotes. On the interval -pi < x < pi Homework Equations tan(2 sin x) The Attempt at a Solution sin(2 sin x)/cos( 2 sin x) Set cos( 2 sin x) = 0 2 sin x = arccos(0) = pi/2 2 sin x = arccos(0) = -pi/2 x = +-(arcsin pi/4)...

Homework Statement Fin the value of arccot(pi/4) Homework Equations unit circle The Attempt at a Solution I honestly can't believe that I'm stuck on this as this shouldn't stump me. My logic is that since its inverse cotangent then its related to inverse tangent and so the...

Suppose we want to find: $$\int \frac{1}{\sqrt{x^2-a^2}}\,dx$$ Trig Substitution: $$=\ln \left| x+\sqrt{x^2-a^2} \right|$$ Hyperbolic Substitution: $$=\cosh^{-1}\left({\frac{x}{a}}\right)=\ln\left({x+\sqrt{x^2-a^2}}\right)$$ I know this is super minor, but how are they equivalent when one...

Homework Statement lim x->0 sin4x/2x Homework Equations lim x->0 sinx/x =1 The Attempt at a Solution can I write lim x->0 sin4x/2x as sinx/x * 4/2 = 1*2 or am I missing a step ?

I have a question on finding the counter clockwise angle the vector difference B-A makes with the +x axis I already have the components of vector difference for B-A and I have checked that they are correct they are 2.77,-5.95 I started with doing the tan function (opp/adj) which was -5.95/2.77 I...

Proving identities is a pain! Thanks in advance, guys! Homework Statement 1. 1 + sec^(2)xsin^(2)x = sec^(2)x 2. sinx/1-cosx + sinx/1+cosx = 2cscxHomework Equations The Attempt at a Solution For the first problem, this is the best I got: 1 + sec^(2)x(1-cos(2)x) For the second problem, I...

Homework Statement Prove that [tan(a) + 1][cot(a+pi/4) + 1] = 2 Homework Equations [tan(a) + 1][cot(a+pi/4) + 1] = 2 The Attempt at a Solution This was very hard, I tried my best at expanding. [tan(a) + 1][cot(a+pi/4) + 1] = tan(a)cot(a+pi/4) + tan(a) + cot(a+pi/4) + 1...

I will try to be as objective as possible and not inflate my post with excuses. I am currently taking a college trig course, and I am doing badly--this might turn into a rant, so be forewarned. I am going to a CC where I have been doing well. My goal is to transfer to an UC and major in physics...

Homework Statement In integration, we are allowed to use identities such as sinx = \sqrt{1-cos^2x}. Why does that work, and why doesn't make a difference in integration? Graphing \sqrt{1-cos^2x} is only equal to sinx on certain intervals such as(0, \pi) and (2\pi, 3\pi). More correctly...

In integration, we are allowed to use identities such as $$sinx = \sqrt{1-cos^2x}$$. Why does that work, and why doesn't make a difference in integration? Graphing $$\sqrt{1-cos^2x}$$ is only equal to sinx on certain intervals such as$$ (0, \pi) $$and $$(2\pi, 3\pi)$$. More correctly, shouldn't...

So I have several problems that ask me to find all points of intersection algebraically, but I haven't been able to make much headway on most of them. [SIZE="3"]The first problem Homework Statement Find all the points of intersection algebraically of the graphs of ... on the interval [0...

Homework Statement 4/PI = 2sin(x) - sin(2x) Homework Equations 4/PI = 2sin(x) - sin(2x) The Attempt at a Solution I have no clue how to do this. This is part of an integration problem for average values. I need to solve for f(c). I know the answer is 1.238, and 2.808.

Homework Statement Homework Equations — The Attempt at a SolutionC) Principal domain: -\dfrac{\pi}{2}\leq 2x^2+x-1\leq \dfrac{\pi}{2} -1.41099 \leq x \leq 0.91099 Next: \sin(2x^2+x-1)=\dfrac{2}{5} 2x^2+x-1=\arcsin(\dfrac{2}{5}) x_1=-1.1265; x_2=0.62650 Since...

I read somewhere that: sqrt(a^2-x^2), you can use x = asinx, acosx sqrt(a^2+x^2), you can use x = atanx (or acotx), asinhx sqrt(x^2-a^2), you can use x = asecx (or a cscx), acoshx When would it be beneficial to use a hyperbolic trig substitution as oppose to the regular trig substitutions (sin...

Im in the process of reviewing for my FE and found an online PDF of the older Lindeburg book while I wait for the new one. While running through the trig section review problems, I came to problem 14. Which is summarized as follows: looking at the top of a flagpole you notice the angle of...

I was stuck for an hour trying to do this calculus 1 problem. Think I figured it out but it's a even problm. Find the absolute maximum and absolute minimum values of f on the given interval. f(t)=t+cot (t/2), [pie/4,7pie/4] f'=1-(1/2) csc^2 (t/2) So 1=1/2*csc^2 (t/2) 2=csc^2...

Please forgive me as I may have to edit this post to get the equations to show properly. I am doing some work with AC circuits and part of one of my phasor equations has this in it: \frac {2i} {1+cos(θ) + i sin(θ)} - i , where i is the imaginary number \sqrt{-1}. However, knowing the...