What is Trig: Definition and 1000 Discussions

Hi all. I have to solve this simultaneous trig equation and I am stumped. Can anybody give me a worked solution please? b*cos 30 = 1375*cos theta (i) b*sin 30 + 1375 sin theta = 1500 (ii) I end up with: b= 1375cos theta / cos 30 substituting into (ii) 1375 cos...

Homework Statement This is taken from a much larger problem, but I only need the answer to one particular question. Please help me understand why the height that a pendulum swings is r(1-cos\theta) where r is the length of the string and theta is the angle it swings through.Homework Equations...

Homework Statement Indefinite Integral (x^3)sqrt((x^2)+4)dx Homework Equations With an x= 2tan@ and dx= 2 (sec^2)@ d@ The Attempt at a Solution I get to 8(tan^3)@(sqrt((4tan^2)@+(8sec^2)@d@ Simplified down to 8(tan^3)@(sqrt((12tan^2)@+8d@ After that I'm stuck The...

Homework Statement tan 2x = 8cos^2 x - cot x. Solve where x 0 ≤ x ≤ pi/2 Homework Equations The basic trig identities The Attempt at a Solution I tried many different things which all eventually led to no solution. Firstly I tried solving the problem as I would a rational...

Homework Statement the problem is: tan(theta) = cos(theta) find theta: -pi < theta < pi Homework Equations tan(theta)=sin(theta)/cos(theta) sin^2(theta)+cos^2(theta)=1 The Attempt at a Solution

First off, this isn't a homework question. I need a solution to the following in terms of \theta. I don't have access to any math software, it's been a number of years since I've done any serious trig, and when I try to solve it on paper it turns into a cluster**** of confusion. If anyone can...

Homework Statement Homework Equations The Attempt at a Solution The part I don't understand is what would be substituted (if anything) for the 24s? How will that be implemented to solve for the periods of time?

Homework Statement We are being asked to evaluate the inverse trig function sin^-1 (1/ sqrt(2)). Homework Equations The Attempt at a Solution I have no clue where to start. I have the unit circle, which makes sense to me if it was a trig function of a trig function, but when it's...

Homework Statement A searchlight is rotating from a point 'P' positioned 50m from the prison walls. The rotation of the light is represented by the equation d = 50sec2pi(t), where d is the distance in meters, from the light to the wall, and 't' is time in minutes. a) graph the the path...

Homework Statement A pedulum, which is 0.5 m long, swings back and forth. The angle of it's displacement from it's original position is modeled by: Theta = 1/4Sin(Pi/3) IN the first 4 seconds, when will the vertical displacement of the pendulum be 1 cm? The Attempt at a Solution What I...

Homework Statement How would you prove: sin4x/ 1-cos4x * (1-cos2x/cos2x) = tanx It was our Thinking and Inquiry question on our test today and I didn't know how to prove it. The Attempt at a Solution I'm not sure if I was headed in the right direction but this is what I did: LS...

Homework Statement Solve for θ. 2sinθcosθ + 1 - 2sin^2θ = 0 Homework Equations The Attempt at a Solution I tried factoring, but I don't know how to continue with 2 diff ID's in one equation. I don't know how to simplify it so that everything is in terms of one similar Identity. :\

Homework Statement Sorry for the long intro: An object is propelled up at angle theta 45 deg. < theta < 90 deg. to the horiz. with initial vel. of V0 m/s. from the base of a plane that makes an angle of 45 deg. with the horiz. If air resistance is ingored, the distance, R, traveled by...

Homework Statement I will ask two questions since they are both under the same lesson. 1) Determine exact solutions for each if domain is xe [0, 2Pi] 2tan^2x -12 = 0 2)Solve the following equations on interval xe [0, 2Pi] sin x - sinxtanx = 0 Homework Equations There aren't...

Trig Functions - "When wil object be 9cm below 0?" Homework Statement Here is the background information: A weight hanging from a spring is set in motion by an upward push. It takes 10 s for the weight to complete one cycle from moving 12 cm above 0, then dropping 12 cm below 0...

Proving trig identities I have 2 more this time, thanks for the time! Homework Statement -sin^2x-sin^2y+1=cos(x+y)cos(x-y) Homework Equations Compound, double, pythagorean, reciprocal, quaotient, etc. The Attempt at a Solution R.H.S. cos(x+y)cos(x-y) =...

Homework Statement Small ball fastened to a piece of string 0.33m in length. The ball is displaced by 60 degrees from the vertical. What is the height of the ball at this point?Homework Equations sin? cos? tan?The Attempt at a Solution This is part of a bigger physics question in which I need...

Homework Statement tanx=csc2x-cot2x Homework Equations Quotient, Reciprocal, Pythagoreans The Attempt at a Solution 1/sinx + 1/sinx - cosx/sinx - cosx/sinx = 2/sinx - 2cosx/sinx = (2-2cosx)/sinx STUCK~

start point (1-Exp[-i x])^2, (i^2 = -1) finish point Sin^2(x)

integral of xarcsinx dx integration by parts and a trig sub by parts I get (x^2)/2 arcsinx - integral (x^2)/sqrt(1-x^2) after that trig sub and i get integral of sin^2 then I used the double angle identity so integral of 1/2 - the integral of (cos2)/2 so i get 1/2...

Homework Statement Ok so I found out last time that the derivative of the function they asked me to find was: \frac {dF}{d\theta} = \frac { - \mu^{2}Wcos(\theta)+\mu W sin(\theta)} { (\mu sin(\theta) + cos (\theta))^{2}} and now they are asking me when is this 0, specifically they...

Homework Statement An object with weight W is dragged along a horizontal plane by a force acting along a rope attached to the object. If the rope makes an angle θ with the plane, then the magnitude of the force is given by the following equation, where μ is a constant called the coefficient...

I am having some issues with going about finding the max and min of trig functions over a set interval. Normally with finding the max and min of a function over an interval the first thing that I do is find the derivative of that function, Then i set the derivative to 0 and solve to find the...

Hey all, hope you could help me, would be very gratefull if you could. Homework Statement Show that sin(x) + cos(x) = √2sin(x + π/4) Homework Equations sin(x+z) = sin(x)cos(z)+sin(z)cos(x) The Attempt at a Solution Ive been doing some of these trig identity problems without an...

Solving trig function... Homework Statement given, csc(6b+pi/8) = sec(2b-pi/8) solve for bHomework Equations The Attempt at a Solution I managed to simplify it to: cos(2b-pi/8) = sin(6b+pi/8) How would i solve for b :confused: well i know that sinx = cos(pi/2-x) so... cos(2b-pi/8) =...

Homework Statement ∫√(2+cos3(t)) dtI should perhaps have tried to get the lower and upper limits of this integral (it's defined), but all I'm wondering about is how to calculate the integral. I don't need the answer, but if someone could just point me in the right direction. I've tried...

Homework Statement h(x) = (sin2x)(cos2x) Homework Equations I attempted to use the product rule: (sin2x)(-sin2x)+(cos2x)(cos2x) = cos22x-sin22x The Attempt at a Solution The book has the answer at 2cos4x, which I obviously didn't get. I've retraced my steps and while unsure...

Homework Statement a right triangle. hypotenuse is 10, the opposite is 8, and the adjacent is 6 Sine .6 Cosine .8 Tangent .75 i need to find angle A (aka Alpha in the problem) With out using a graphing or scientific calculator. Homework Equations i was told to use...

I couldn't figure out how (*) derived. How can the underlined part's sine function vanishes? http://img149.imageshack.us/img149/8642/asfdg.png Uploaded with ImageShack.us

Homework Statement find all values of x in the interval [0, 2pi] that satisfy the equation 2cosx + 1 less than or equal to 0 Homework Equations None. The Attempt at a Solution for when 2cosx+1=0 cosx=-1/2 x= 2pi/3, 4pi/3 but what about the values for when 2cosx + 1 is less then...

Homework Statement sin(2x)-cos(2x)=sqrt(2)sin(2x+Api), then the number 0 < A = ____ < 2 Homework Equations http://bit.ly/9njiUW <-- trig reference sheet with formulas and identites The Attempt at a Solution So I start with the left side of the equation and attempt to make it...

Homework Statement Determine sin(arctan(3)) The Attempt at a Solution I do not know how to start this. No special triangles : (.

Homework Statement Find the trigonometric ratios sin\theta, cos\theta, tan\theta for the angle \theta = 14\pi. If a ratio does not exist or is undefined, write "DNE". The Attempt at a Solution I know that the other equivalent angle for 15pi is just pi. But I do not know how to write the...

Homework Statement f(theta)=2sec(theta)+tan(theta) The Attempt at a Solution I found the derivative and set it equal to zero and to reduce writing I substituted x for theta f'(x)=2sec(x)tan(x)+sec^2(x) sec(x)[2tan(x)+sec(x)]=0 My question is what are the critical numbers? do the...

Homework Statement edit* It says Verify the formulas in problems arcsin(z) = -iln(iz ±sqrt(1-z^2)) arccos(z) = iln(z ±sqrt(1-z^2))tanh-1z = (1/2)ln((1+z)/(1-z)) The Attempt at a Solutionyeah, my prof just threw it at us, all i have is nothing... absolutely nothing. I don't know why he does...

Homework Statement For two waves in superposition, we have, let say \[y_{1} = Asin(kx-wt), y_{2} = Asin(kx-wt+\Phi )\] We use the trig identity sin A + sin B to simplify the combination Whereas for standing waves, we use the trig identity sin(a +/- b) to combine the result. As I...

Homework Statement is there a way to solve lim (x->0) \frac{x - sinx}{x^{3}} using the fact that sinx / x = 1 or is it much more complicated.. I've tried to break it down into sinx/x everyway i can think of with no luck..

Homework Statement solve the following equation for x in the interval [0,2pi) 2Cos^2(2x) + 1 = 3Cos(2x) Homework Equations Cos(2x) = 2Cos^2 (x) - 1 The Attempt at a Solution 2Cos^2(2x) + 1 = 3Cos(2x) 2Cos(2x)Cos(2x) + 1 = 3Cos(2x) 2Cos(2x) + 1 = 3 2(2Cos^2 (x) - 1) - 2...

Homework Statement lim t--> 0 cos(1-(sint/t) Homework Equations lim theta-->0 sin(theta)/theta =1 The Attempt at a Solution I usually don't have a problem with these limits, but I've never done 1 with a trig function inside another trig function. So I don't know how to begin this one.

Given the number of molecules hitting unit area of a surface per second with speeds between v and v +dv and angles between \theta and d\theta to the normal is \frac{1}{2} v n f(v)dv sin \theta cos \theta d\theta show that the average value of cos \theta for these molecules is \frac{2}{3}. I...

Homework Statement The Attempt at a Solution No attempt, don't even know where to start. I get a point... I can draw a triangle out of it. I can figure out the X and the Y. I know the 6 equations... Sin, Cos, Tan, and the opposites Cosecant, Secant, and Cotangent... I know...

Homework Statement sec^2x - 3secx + 2 < 0 Homework Equations The Attempt at a Solution sec^2x - 3secx + 2 < 0 ok so this can be written as, (secx - 2)(secx -1) < 0 this means secx is between 1 and 2 right ? secx = 2 and secx = 1 would we find all the solutions that's...

Homework Statement Find all solution for x in the interval [0, 2pi) 2cos(3x) - 1 = 0 Homework Equations The Attempt at a Solution 2cos3x = 1 cos3x = 1/2 since x = [0,2pi) therefore, 3x is [0,6pi) so.. here is my problem i know that cosx =1/2 is 1/3pi, and...

Homework Statement how do you go about solving the equation lim (t->0) 2t / (sin(t)) - t the answer in the text is significantly different than what i get.. i can get most of the other trig limits using the fundamental limit etc.. but this one I am stuck ? i may be way over...

Homework Statement tanx + 3cotx = 4 Homework Equations The Attempt at a Solution Heres my attempt: tanx + 3/tanx - 4 = 0 (tan^2x -4tanx + 3) / tanx = 0 tan^2x - 4 tanx + 3 (tanx - 3 ) (tanx - 1 ) = 0 tan = 3, tan = 1 im not sure about tan = 3, but for tan = 1 ...

How would one go about solving the following equation? 242= 290cos(theta) + 187cos(phi) 0 = 290sin(theta) - 187sin(phi) I have tried squaring both sides of both equations and adding them, and then using cos2x + sin2x = 1 to narrow some stuff down, and basically only found that: phi +...

Homework Statement Given 0 <= a <= b show that, a <= sqrt(ab) <= (a+ b / 2) <= b Homework Equations a * b <= a^2 / a*b <= a* a The Attempt at a Solution I think i know where I am going but i wanted to make sure if its correct so far. So we know that...

Homework Statement Find the general solution of: a) sin x = 1/\sqrt{2} b) cos x = 0.5 The Attempt at a Solution a) x = asin(1/\sqrt{2}) x = (π/4) + 2nπ b) x = acos(0.5) x = π/3 + 2nπ Basically, my strategy was to solve for the basic angle, and then add multiples of the...

Homework Statement lim x->0 (1-cosx)/sinx Homework Equations (sinx)/(1+cosx) = (1-cosx)/(sinx) sinx/x = 1 The Attempt at a Solution Well, I know I need to change my original limit, as I cannot let the denominator be 0. I usually try to factor out things, but there is nothing to...

Homework Statement Given that cos C = 12/13 where C is a reflex and sin D = 3/5 where D is acute, find the exact value of cos ( C + D ). Homework Equations The Attempt at a Solution I used the Addition Formulae: cos(A+B) = cosAcosB-sinAsinB cos(12/13)cos(2/5) -...