Trigonometry Definition and 662 Threads

1) A piece of paper is in the shape of a sector of a circle. The radius is 8cm and the angle at the centre is 3pi/4 radians. The straight edges of the sector are placed together so that a cone is formed. Show that the base of the cone has a radius of 3cm. Find the area of theh curved surface of...

Homework Statement Find lim x -> 0 \frac{sin x}{sin\frac{x}{2}} The Attempt at a Solution Since period of sin 2(x/2) is T/2 compared to period T of sin (x/2) sin 2(x/2) nears twice the value of sin (x/2) for all values of x approaching zero. Therefore lim x -> 0 \frac{sin...

I am learning about the unit circle and I am a bit confused. So, I have my circle drawn with radius 1 and I sketched a right angled triangle inside it so that the hypothenuse has a length of 1. I think what is making me confused is the meaning of sine, cosine and tangent. They are...

Homework Statement Hi I am doing a maths past paper and I would like some help to understand where part of the solution came from. The part I do not understand is the bit at the end which says tan\alpha = 5\pi/4. It would be great if someone could help me understand where this came from...

Homework Statement Given the equality \frac{sin^4(x)}{a} + \frac{cos^4}{b} = \frac{1}{a+b} Prove that : \frac{sin^8(x)}{a^3} + \frac{cos^8}{b^3} = \frac{1}{(a+b)^3} The Attempt at a Solution I cubed on both the sides of the 1st equation and solved a bit, reaching no where. Then I...

This is no homework exercise, just plain curiosity for an exercise, so give it lower priority. Homework Statement Is it possible to solve tan(x) = 3 without the use of a calculator? The knowns: 1) It originaly came from trying to solve 1/(cos^2) -2tan = 4. 1 = cos^2+sin^2 so this...

Homework Statement If cos(x) = -¾ or cos = ½ then the value of M and N in the equation Mcos^2(x) + Ncos(x) – 3 = 0 are what? Homework Equations Identities I can use: csc(x) = 1/sin(x) cot(x) = 1/tan(x) sec(x) = 1/cos(x) tan(x) = sin(x)/cos(x) cot(x) = cos(x)/sin(x) sin^2(x)...

Homework Statement I need help with trigonometry proofs. the question asks me to prove the following and show all my steps. Prove that: Tan(x) – ½sin(2x) = tan(x)sin2(x)Homework Equations I don't know :( The Attempt at a Solution No attempt as I don't get it.Any help at all would be...

a=4, b=1, C=120* do you agree, that if you do not round until the final amswer, that angle B = 10.90? rounded to the nearest hundredth? correct answer given is 10.92...

OK at the 2 year college here, they offer ONLY trig , and you take that after college algebra, and before you take calculus, and the counselors at the 2 year college all say that, trig and precalculus mean the same thing there, which is weird, because, then if you look at the classes offered at...

How big of a role does trigonometry play in physics? I am learning trigonometry as of this instance and I'm finding it to be incredibly interesting and fascinating.

I am a first year engineering student and i am starting to really understand/be very interested in math. I have started proving random theorems after being intrigued by things in class and am really appreciating things like the fundamental theorem of calculus. I am very curios about how...

Homework Statement Hi, This isn't a homework question, I am having a bit of trouble with some Trig equations. If you are worried that you are answering a homework question please give me the solution to a similar question. Homework Equations When we have a trig equation like sec2X + tan2X =...

Homework Statement limit x to phi/2 of: (2 + cos 2x - sin x) / (x. cos x + x. sin 2x) Homework Equations limit and trigonometry The Attempt at a Solution Using differentiation, I got zero as the answer. But I am not able to do without differentiation (2 + cos 2x - sin x) / (x...

Homework Statement Homework Equations The Attempt at a Solution i have no idea how to start

Homework Statement [2sin3y + (sin3x-siny)(cos4y-cos2y) : cos(x-y)-cos(x+y)] : sin^2x Homework Equations sinx-siny=2 * cos x+y/2 * sin x-y/2 cosx-cosy=2 * sin x+y/2 * sin x-y/2 cos(x-y)=cosxcosy+sinxsiny cos(x+y)=cosxcosy-sinxsiny cos2x=cos^2x-sin^2x The Attempt at a Solution...

Given R = \sqrt{d^2 + z^2} and \cos \alpha = \frac{d}{R} find \int \frac{1}{d^2 + z^2}dz The answer given is \frac{1}{d}\tan^{-1}(\frac{z}{d}) I only know that I have to convert the denominator to secant squared, which integrates to a tangent. However, I don't know how the tangent...

Bodybuilder “Hulk” Heise is doing leg curls on a Cybex machine. “Hulk” gets stuck (see figure) with 90° angle at the knee joint. The force exerted by the machines (FA) on his leg is 500 N, directed at an angle of 55° (angle α) relative to the tibia, and the distance from “Hulk’s” knee joint to...

Homework Statement Solve limx->0 (sin-1 x) / x Homework Equations given limx->0 (sin x) / x = 1 The Attempt at a Solution

Homework Statement The sun was shining in the yard of engineer Jack Smith. Jack was reading in the shadow cast by the pine tree planted by his grandfather Tom Smith. The length of the horizontal part of the shadow was 6.0 m and the height of the vertical part of the shadow on the wall was 3.6...

Why aren't there trigonometric functions for elliptic geometry? There is trigonometry for circles and hyperbolas, but why not ellipses?

Homework Statement When the sun is 74° above the horizontal a vertical flag pole casts an 8.5m shadow on the horizontal. Find the shadow cast when the sun lowers to 62° above the horizontal. Homework Equations The Attempt at a Solution I drew the following diagram...

Homework Statement (1) Real variables x and y are related by the equation 3ln(y +4) = 2ln(x +2) − 2ln(x +9)+3ln(x^2 − 1). Determine the range of values of x and y for which the expressions on each side of this equation are defined. Find y explicitly as a function of x, that is...

Homework Statement a. \int cos(\pi~sin~x)~dx b. \int x~cos(\pi~sin~x)~dx Homework Equations integration The Attempt at a Solution can anyone help me getting started? Thanks

hello again. :smile: I have 2 trigno "solve the equation for" problems which I am having difficulty with. Q.1) This came in 2 parts. I've done the first part but I'll post it anyway as it is important for the next part (where I'm having difficulty). i) Show that equation 4sin^4\theta...

I need help with a question and I'm totally stuck at this! My friends can't help me so you are my last way out! Prove ∫sin^n x dx= -(1/n)cos x sin^n-1 x + ((n-1)/n) ∫sin^n-2 x dx Thanks for your time! Sincerely :)

Homework Statement Find the exact solution for: x^2 - 2cosx = 0 Homework Equations The Attempt at a Solution There aren't any constants to bring to the other side, so I'm not sure how to solve for x.

Homework Statement I have no idea how to figure this out. Please help!:) Complete the square to find the center and radius of the circle: (equation of a circle:(x-h)^2 + (y-k)^2 = r^2, where (h,k) is the center and r is the radius) y^2+12y=17-x^2+2x (^2 = squared)

Hi everyone, I've tried googling how to calculate a straight line distance on a sphere. I got no answers for it though T_T. I was able to find the great circle distance and parallel's already. I'm given 2x points with lats/longs and ellipsoidal heights. Can anyone guide me in the...

Homework Statement Hi there. Where, I got this exercise. I have a ball attached to an ideal rope with longitude L, moving on a circle with speed V on a circular trajectory with radius R over an horizontal plane. So it asks me to express the subjected force over the rope as a function of the...

Homework Statement (tanx - cosecx)2 - (cotx - secx)2 = 2(cosecx - secx)Homework Equations tanx = sinx/cosx cotx = 1/tanx = cosx/sinx cosecx = 1/sinx secx = 1/cosx The Attempt at a Solution LHS = (tanx-cosecx)(tanx-cosecx) - (cotx-secx)(cotx-secx) = tan2x - tanxcosecx - tanxcosecx +...

The coolest fact in trigonometry that you learn way too late... So I just spent the last 12 hours learning trig (occasional food breaks). I just want to share with you something really, really, really, really, awesome. Check this out, you're going to be blown away The law of...

Does this pic make sense? If pi is equal to 3.14, how come it seems drawn at where 1 supposed to be? [PLAIN]http://img210.imageshack.us/img210/6190/sine.jpg

Hi, I have a problem that arose in one of my courses that I've gotten stuck on. I reduced it to two equations in two unknowns but can't get any further. I've apparently forgotten all the trigonometry I used to know. C = Acos(x) + Bcos(y) 0 = Asin(x) + Bsin(y) where A,B,C are known but...

Homework Statement show that (a cos A - b cos B) / (b cos A - a cos B)= cos C if ABC is triangle Homework Equations trigonometry identity The Attempt at a Solution A + B + C = 180o A = 180o - (B+C) cos A = - cos (B+C) substitute cos A to the LHS: (- a cos (B+C) - b cos B) / (b cos A - a cos...

Homework Statement evaluate sin (π / 62) . sin (15π/62). sin(23π/62). sin(27π/62) . sin(29π/62) Homework Equations trigonometry The Attempt at a Solution Tried to change it to cos but failed, tried to use 2 sin A sin B identity and failed again Thank you very much

Homework Statement Let A,B,C be three angles such that A=45 (degrees) and tanBtanC=p. Find all possible values of p such that A,B,C are the angles of a triangle. Homework Equations The Attempt at a Solution I got an expression for cos(B-C)= (1+p)/{(p-1)√2} My book says this-...

Homework Statement [PLAIN]http://img530.imageshack.us/img530/5062/dgsdgsdgs.jpg what is h?? Homework Equations tan x = sin x/ cos x cos x = adj/hyp sin x = opp/hyp The Attempt at a Solution uh I am not even really sure where to start. i haven't done trig in a really really long...

Homework Statement P1 sin 2x + sqrt(2) sin (x - (pi/4)) = 1 P2 Two sides of a triangle are 5cm and 9cm long. The ratio of the opposite angles is 1:3. Determine the angles and the length of the third side of the triangle! Homework Equations sin(2&) = 2 sin&cos& sin(& - §) = sin&...

Homework Statement I can't find way to solve \frac{Sin25 * Sin65}{Cos 40} Homework Equations The Attempt at a Solution I looked trough allformulas i have I came up with: \frac{Sin25 * Sin65}{Cos 40} = \frac{Sin25 * Cos25}{Cos 40} But then found that formula is: Sin 2a =2{Sina * Cosa} Which...

Homework Statement Find all values of θ in the interval 0 ≤ θ ≤ 360 that satisfy the equation sin 2θ = sin θ Homework Equations sin2θ = 2sinAcosA The Attempt at a Solution I'm a little confused on how to start off knowing sin2θ is equivalent to 2sinAcosA, would you factor this?

Homework Statement A parallelogram's two sides are 24 feet amd 30 feet. The measure of the angle between these sides is 57 degrees. Find the area of the parallelogram, to the nearest square foot. Homework Equations area = 1/2 (a) (b) Sin C The Attempt at a Solution I'm thinking...

Hi, I'm trying to delve back into the world of physics. Unfortunately, i haven't done any type of geometry or trigonometry in many years. So, my question is, what are the best (ideally free; I'm a poor grad student after all :-) books to learn plane euclidean geometry and trigonometry? I figure...

Homework Statement In the diagram below, KW = 6, Kt = 5 and m<KTW = 90. What is the measure of angle K, to the nearest minute? Below is the website for this question because this is one of the questions from the algebra 2 and trigonomentary. This is question 23...

Homework Statement The orbits of Earth and Venus are so close to being circles that on the scale of the diagram below, you would not be able to tell they were not circles. a) Do you think the assumption that the orbits are circles has a significant effect on the result? b) Where in the...

I find this statement confusing from Wikipedia: sin(y)=x\Leftrightarrow y=arcsin(x)+2k\pi\ \forall\ k\in\mathbb Z Is this statement false? "arcsin(x)" gives the principal value:[\frac{-\pi}{2},\frac{\pi}{2}]. Therefore,specifically, "arcsin(x)" gives \frac{\pi}{3}\text{ but...

Homework Statement Hi, I scanned some few questions from my Trigonometry book that were giving me giving me problems. I tried them but I could not understand what they were asking for.. Please point me in the right direction and I will do the rest. Homework Equations The Attempt at...

Homework Statement Consider P(2,1,3) and the line L: \begin{Bmatrix}x-y-5=0 \\z-1=0 \end{matrix} a) Find the equation of the line that pass through P and cuts L on a perpendicular angle. b)Finds the points A and B in L in a way that PAB being an equilateral triangle. Homework Equations...

1. sec^4 x + sec^2 x tan^2 x - 2 tan^4 x = ? The possible answers are: a. 4 sec^2 x b. 3 sec^2 x - 2 c. sec^2 x + 2 d. tan^2 x - 1 Homework Equations No idea. The Attempt at a Solution I'm not sure where to begin here. My book first doesn't cover anything above...

Homework Statement A wireless aerial attacheed to thee top of thee mast 20m high exerts a horizontal force of 600N on it.The mast is supported by a stay -wire running to the groung from a point 6m beow the top of the mast, and inclined at 60 degrees to the horizontal. Assuming that the reation...