Trigonometry Definition and 664 Threads

Homework Statement The diameter of each wheel of a bicycle is 26 inches. If you are traveling at a speed of 35 miles per hour on this bicycle, through how many revolutions per minute are the wheels turning ? Homework Equations The Attempt at a Solution I have no idea how to solve...

Homework Statement Show that the solutions of the equation 2sin(z) + cos(z) = isin(z) are given by z = (n\pi-\frac{\pi}{8}) - \frac{1}{4}iln2Homework Equations e^{iz} = cos(z) + isin(z) sinz = \frac{1}{2i}(e^{z}-e^{-z}) z_{1}^{z_{2}} = e^{z_{2}lnz_{1}} lnz = lnr...

Homework Statement Express cos^4Θ.sinΘ in the form asinΘ+bsin3Θ+csin5Θ Homework Equations cosrΘ = 1/2(z^r + z^-r) sinrΘ = 1/2i(z^r - z^-r) The Attempt at a Solution So far I think I have this. 32i(sinΘ)(cos^4Θ) = (z-z^-1)(z+z^-1)^4 I am unsure how to multiply and manipulate...

So I'm not really sure how to go about this problem. I've attempted letting x = a few things. 4sinx, and 4tanx. Maybe trig substitution is not even the way to go. Could someone push me in the right direction?

Sorry, for overloading you guys, but I just can't get my head around these! Question 1 Homework Statement Show that, when restricted to the domain [-1,1], g has an inverse function. Use a definition of a theorem, a graph will not be accepted. Homework Equations g(x) = x/(x^2 + 1)...

(CHALLENGING!)Trigonometry / geometry proof Hey guys I've spent a couple hours on this without even coming close. I'm hoping someone here can drop me a hint. From the above image I need to proof that GL is R(THETA) in length. The only other information I have is that GT extended is a type of...

[b]1. Hi Its the bit (c) where i am stuck at although it doesn't look much complicated, for all i know is that max value for cos =1 , so cos inverse becomes 0. The answer on the mark scheme is theta = 326 which i can't figure out.Thanks Homework Equations The Attempt at a Solution

Solve 3\cos\frac{3x}{2}=\cos\frac{x}{2} I am interested to know how to go about solving such an equation where the coefficient of cos(x) is not equal to 1. I know how to solve \cos\theta = \cos\alpha, \mbox{ it is just} \theta = 2n\pi +/-\alpha I teach various maths subject to myself, then I...

Homework Statement sin90degrees +tan45degrees Homework Equations The Attempt at a Solution my answer is 0 but my textbook says its 2. I don't understand how 2 is the answer.

Homework Statement If sin x = 1/3 and sec y = 5/4, where x and y lie between 0 and pi/2, evaluate the expression. sin2y cos2y Homework Equations 2siny = 2siny*cosy? cos2y = cos^2 y - sin^2 y? The Attempt at a Solution I think sin2y goes to 2siny*cosy. I know what sin x...

Homework Statement tansquaredB=4 solving for B Homework Equations This is algebra applied to Trigonometry, through simplification, to arrive at several different answers involving the degrees of angles. I hope this applies to Physics since physics is "applied Mathematics"...

Homework Statement Differentiate the following cos^2 x The Attempt at a Solution \frac{d(cos^2 x)}{dx} = 2 (-sin^{2-1} x).\frac{dx}{dx} = 2 (-sin x).1 = -2 sin x But the answer given is- -2 cos x sin x Can you please tell me what's wrong !

Homework Statement Find the maximum and minimum values of 4cos\theta-3sin\theta. Homework Equations I have no idea. The Attempt at a Solution I have no idea how to do this question Please help me!

Homework Statement I have to find the measures of the angles x & y. Homework Equations Sine Law Cosine Law The Attempt at a Solution First thing I tried to do was find the measure of the angle @ A. a/SinA = c/SinC 66/SinA = 25/Sin10.5 and then I end up with 28...

Hi, This is a problem that has been very confusing for me and I feel it could be because I am misinterpreting the wording: A tree standing (vertically) on a slope inclined at an angle of 11° to the horizontal casts a shadow of length 15m up the slope. If the angle of elevation of the sun...

HELP! trigonometry Homework Statement without using calculator: prove that: sin18 = √5-1/4 Homework Equations Double-angle formulae sin 2a = 2sin a.cos a cos 2a = cos^2a - sin^2a = 1 - 2sin^2a = 2cos^2a - 1 sin^2 a + cos^2 a=1 The Attempt at a Solution let 18=a sin a = sin(90 -...

Determine an exact value of b such that csc(6b+π/8)=sec(2b-π/8). Just to clarify, π is pi. This question deals with equivalent trigonometric expressions. I have absolutely no idea how to solve this problem. Please provide me with explanations. Thanks in advance.

Homework Statement a = 1/sqrt(29) * (-2*sint, 0, -2*cost) length of a is? Homework Equations The Attempt at a Solution ignoring 0, we have sqrt{[(-2*sint)/sqrt(29)]^2 + [(-2*cost)/sqrt(29)]^2}. I get 2/sqrt(29) but answer is [2*sqrt(2)]/sqrt(29). Can anyone do this step by step...

Homework Statement x = (-4\pisin\pit, 4\picos\pit, 1) what is the length of x?Homework Equations The Attempt at a Solution Well, I do realize that length of something is calculated by sqrt(x^2 + y^2) etc. However, when I plug in the numbers above, I get sqrt(16\pi^3 + 1), but the answer is...

Dear all, I would like to evaluate \int\frac{1}{1-2sin\left(x\right)}dx Firstly, I make use of the Weierstrass substitution method by letting: u=tan\left(\frac{x}{2}\right) and therefore sin\left(x\right)=\frac{2u}{1+u^{2}} and dx=\frac{2}{1+u^{2}}du Eventually I can...

I'm currently in first year calculus, and I'm having trouble remembering all my trig for use in derivatives. I have some stuff memorized, obviously soh cah toa, and the derivatives of the six trig functions. i.e. derivatives of sinx = cosx cosx = -sinx tan = sec^2(x) etc... but...

Homework Statement In a certain collision problem the kinematics are determined by the following three equations: u=u1cos(@) + SQRT(2) * u2 u1sin(@)=SQRT(2) * u2 0.5mu^2=0.5mu1^2 + 0.5(2m)u2^2 Use the first two equations to express u1 and u2 in terms of u, sin(@) and cos(@). Then substitute...

1. Homework Statement A drawing shows sodium and chloride ions positioned at the corners of a cube that is part of the crystal structure of sodium chloride. The edge of the cube is 0.281nm in length. Find the distance between the sodium ion located at one corner of the cube and the chloride...

Homework Statement A drawing shows sodium and chloride ions positioned at the corners of a cube that is part of the crystal structure of sodium chloride. The edge of the cube is 0.281nm in length. Find the distance between the sodium ion located at one corner of the cube and the chloride ion...

I was just wondering if anyone could suggest information about the advanced study of trigonometry. I am contemplating getting a degree in mathematics, and I'm currently trying to master the basics of trigonometry in preparation for taking cactus. In looking at all the courses I'll be taking...

Homework Statement Suppose that x=7pi/23 is a solution of the equation sinx= A where A is some constant. Then A must be equal to [blank], and the other solution of the equation in the interval [0,2pi] must be x = [blank]. The Attempt at a Solution So I've plugged the value into my...

Homework Statement For small angles, the numerical value of sin theta is equivalent to tan theta. find the largest angle for which sine and tangent agree. Homework Equations I do not think a equation is need to answer this question. The Attempt at a Solution I honestly couldn't...

Hi, I need a good book for high school Algebra. If possible, Algebra and Trigonometry both in one book. By High School, I mean for age 15-17years. :P I have chosen Algebra and Trigonometry (3rd Edition) by Beecher/Penna/Bittinger. I think its a good book. Please suggest me more books...

Heres the situation, I have a triangle in which i found all 3 interior angles. I also have the length of all the sides and the coordinates of 2 points. I just need to find the coordinates of the 3rd point I am missing. Is there some formula i need to use for this?

Homework Statement i need to find angle BDC and side BC when given that AB = 60m BAC = 64 AC = 124 BD = 130 CD = 145 and to find the area of the whole plot Homework Equations The Attempt at a Solution i have worked out side BC = 111.59 by using the Co-sine rule a^2 =...

Okay, I must admit, my trigonometry is rather awful... anyway, I would like to write out what 1 / 2^2 is equal to in terms of sine, cosine, tangent, and the like is the following correct, or how do I write it correctly (or what would be the correct figures for 0.5^0.5): 0.5^0.5 = a...

Homework Statement Bob heads out into a lake at an angle of 36 degrees, with respect to the shore. If his boat is capable of a speed of 1.7 m/s, how far from land will he be in 7 min and 23 s? Answer in units of m. Homework Equations I have no idea what equation would work for this...

Can someone just check my maths to see if this is correct. Hopefully, this should give the coordinates for a point on a sphere? x = radius x cos(vert angle) x sin(hoz angle) y = radius x cos(hoz angle) z = radius x sin(vert angle) x sin(hoz angle)

Homework Statement solve 3cos(x) + 3 = 2 sin^2(x) where 0 <= x < 2piHomework Equations The Attempt at a Solution 3(cos(x) + 1) = 2 sin^2(x) 3(cos(x) + 1) = 2 (1- cos^2(x)) I've tried this variation, and a couple others but it just does not pan out. Please help. Oh yeah we have a real...

Homework Statement Solve the following equation: (2sinx-1)(tanx-1) = 0 0<x<2pi The answers are listed as : pi/6, 5pi/6, pi/4, 54/4 Homework Equations I'm told the unit circle is used. The Attempt at a Solution I'm attempting to learn this from dijointed class notes for...

Currently, my knowledge of mathematics includes topics through Calculus, Number Theory, and a bit of Linear Algebra. However, what I'm really interested in learning is spherical trigonometry. I understand that spherical trig has diverse apps in astronomy, but that's about the extent of my...

I feel so shamed of myself. I don't know who to blame. The teacher gives the exact same lessons on the book, but never follow how you should answer your trig. problems. I studied all through the week and even late at night. I got a C in the class, but I really want to be a physicist because I...

Trigonometry Basic (URGENT) please help ! Homework Statement SIMPLIFY: sin(x)/cot^2(x) - sin(x)/cos^2(x) Homework Equations Trigonometric identities I think The Attempt at a Solution I got sin(x)cot^-2(x) - sin(x) sec^2(x) ... but the book says the answer is...

Homework Statement Straight line segments are drawn from the fixed point P1(0,1) and P2(3,2) to the movable point P, with coordinates (x,0)on the positive x-axis. Assuming that 0 ≤ x ≤ 3, show that the angle θ between the two line segments PP1 and PP2 is given by the relation: θ=...

Homework Statement As given in the title. The law of cosines, the law of sines, or any other aspect of trigonometry may be used. Ultimately, I need to show that when two triangles have two pairs of proportional sides and the included angles congruent, that they are similar - that is, the...

Homework Statement Find the values of the following, without the use of a calculator, cos(15)+sin(15) Homework Equations sin(A±B)= sinAcosB±cosAsinB cos(A±B)= cosAcosB∓sinAsinB The Attempt at a Solution Without the use of a calculator i had to relate back to the 2 triangles which...

Homework Statement solve, finding all solutions between [0,2pi] tanx=3cotx The Attempt at a Solution It looks like a relatively simple problem if one knew what they were doing unfortunately I do not. I am trying to think of this graphically and I figure that the places were tanx=3cotx...

Homework Statement arcsec([2 * sqrt(3)] / 3) Homework Equations N/A The Attempt at a Solution I know that this is equivalent to saying sec (theta) = [2 * sqrt(3)] / 3 I don't know how to solve for theta in terms of PI. I know sec = hyp/adj and the opp side I found was...

1:... 2:... 3:... 4: Y = A cos(Bx+C)+K Y = A sin(Bx+C)+K I know what A,B,C, and K mean.. and I Also understand that I can get the Period from B.. but, how can I use the information to draw the graph? I think I should use critical points, right? If so, what should I typically use...

Homework Statement A screenshot of the problem: http://img246.imageshack.us/img246/9194/homeworkkd6.jpg Homework Equations Not sure... possibly the dot product of two vectors? v*w = a(1)a(2) + b(1)b(2) The Attempt at a Solution Part of the problem is that I'm not entirely sure...

Hey all, I'm looking for a decent, (and preferably cheap) book, or books, on trigonometry. Something that proves some or all the trig equations we're expected to remember in high school stuff (most of which I've forgotten), but it should also leave room for my curiosity so I can prepare for...

If sinx = -0.40 and tanx > 0, then secx, to the nearest hundreth, is A) 0.92 B) -0.92 C) -1.09 D) 1.09 So I figured that sin^-1 = -23.57817848, but I don't know how to get sec, can someone help!

Intro: Hello, I have spent the last four or so days searching google and this forum and as rich as both are in information and helping. I have found it very hard to get anywhere. Basically I haven't done any Maths/Physics related courses and as a result I am totally stumpped on my Games...

Homework Statement When dealing with periods and amplitudes in trigonometry, are all complete cycles (for cosine, sine, and tan functions) considered to be 360(degrees)? I'm just wondering, because I want to make sure now so that I can apply it to the appropriate questions when the time...

Sorry but i don't know how to use latex yet or to add mathematical symbols somehow. Homework Statement Prove that 1-sin2θ/cos2θ = 1-tanθ/1+tanθ Homework Equations sin2θ = 2tanθ/1+tan2θ and cos2θ =1-tan2θ/1+tan2θ I have allready proved from a previous exercise those two above so...