Trigonometry Definition and 662 Threads

Homework Statement [/B] Solve ##2sin3x.sinx=1##Homework EquationsThe Attempt at a Solution I used the identity ##( cos (A+B)= cos A cos B- sin A sin B), (cos(A-B) = cos A cos B+sinA sinB)→ -(cos 4x-cos2x)= 2sin 3xsinx, (cos 2x-cos4x=1)##now i am stuck , is this correct_ using ##(cos...

Why trigonometric functions are defined for unit circle, here "why" refers to what made them to define it this way, they may have defined it for right triangle only , can you give me a application where sin(120°) or sin, cos , tan of more than 90° is used to find some values like in physics or...

Hi all. I'm a liberal arts graduate looking to enter a statistics masters program (in case it matters). I'm retaking some lower level courses to prove I can do math I wanted to know how much trig is used in Calc II and beyond. I didn't do great in that class (I'm going to retake it) and when I...

$\triangle ABC,\angle B=30^o$ and $\overline{BC}^2-\overline{AB}^2=\overline{AB}\times \overline{AC}$ using trigonometry to prove $\angle C=50^o$

When do we learn about spherical trigonometry and what are its application(mostly in physics) I have read a formula named versed sine = 1- cos(θ) in the trigonometry book by S.L loney, I tried it on google to know more about it and the research made me shocked, haversine(half of versed sine)...

Homework Statement show that 1-t^2/2 <=cos(t) <=1 for 0<=t<=1 Homework Equations Trigonometry knowledge The Attempt at a Solution I don't know how to relate t with cos(t), and I also try to find out cos(1), but there is no result, so how can I start with this problem.

Homework Statement I don't understand how to get CE. Homework Equations Trigonometric identities (maybe) The Attempt at a Solution [/B] First, I start with the cosine rule CB^2 = AC^2 + AB^2 - 2 AC AB cos α (CE/sin(β))^2 = (CE/sin(α))^2 + L^2 - 2 (CE/sin(α)) L cos α which is going to be...

Homework Statement A highway is to be built between two towns, one of which lies 35.0km south and 72.0km west of the other. What is the shortest length of highway that can be built between the two towns, and at what angle would this highway be directed with respect to due west. Homework...

Homework Statement Show that sin 600° . cos 330° + cos 120° . sin 150° = - 1 Homework Equations I know that sinΘ = opposite/hypotenuse and cosΘ = adjacent/hypotenuse. The Attempt at a Solution I am equipped with knowledge about what sinΘ and cosΘ is from right angled triangle. I stand in...

I across a video about how to be good enough at anything within 20 hours. It said that first to get rid of all barriers and the identify The small skills which are used in the thing you're trying to "become good enough at ",in this case in solving trigonometry questions, and grind them...

The problem For ##0 < x < 1 ## . Show that $$ \sin(\arctan x) < x < \tan(\arcsin x) $$ The attempt I know that ## \sin x < x < \tan x ## is true for ## 0 < x < \ \pi / 2 ## x - is by definition the length DA (in radians) I draw a right triangle with sides x and 1 and with hypotenuse ##...

Hi, As told in the problem I drew a figure, Next the magnitude of $$\angle BHL$$ should be found using trigonometric tables. Can you help me to and find the angle BHL (Smile) Many Thanks (Smile)

Hi all, can you show me how to calculate this and breakdown how you get to the answer for me to Understand ,I have been shown what is believed to be the answer from the notes but not a clue How it was reached. Find all the solutions to the following equation at interval 0,6PI cos(x) +...

Homework Statement I want to know how he simplified this expression to tan (theta) Homework EquationsThe Attempt at a Solution

The problem I am trying to write ##-sin 2x + \sqrt{3} \cos 2x ## as ## A \sin(2x+\phi)## without using this formula below ##a sin (x) + b cos (x) = c sin (x+v), \ \ c=\sqrt{a^2+b^2} \ ,\ \ \tan v = \frac{b}{a}## The attempt ##A \sin(2x+\phi) = A \cos(\phi) \sin(2x) + A \sin(\phi)...

I have encountered this equation: ##\cos^2 \gamma = \cos^2 \alpha \cdot \cos^2 \beta## According to the paper, this is a trigonometric identity, but this is the first time I have encountered this. The angles ##\alpha## and ##\beta## are somewhat similar to the components of the distance...

Homework Statement A triangle with a hypotenuse of 13.5 and height of 11.8. Find the measure of angle P. Angle p is on the same line as the 90 degree angle and I found out that it must be sine. Homework Equations sine = opposite/hypotenuse The Attempt at a Solution sin p = 11.8/13.5 sin p =...

Consider ##y=\cos{-x}=\cos x=\cosh ix##. Thus, ##\pm x=\cos^{-1}y## and ##ix=\cosh^{-1}y##. So ##\cosh^{-1}y=\pm i\cos^{-1}y##. Renaming the variable ##y##, we have ##\cosh^{-1}x=\pm i\cos^{-1}x##. Next, we evaluate the derivative of ##\cosh^{-1}x## by converting it to ##\cos^{-1}x## using...

Homework Statement a) Differentiate the following equation with respect to: 1) θ 2) Φ 3) ψ (Ua - Ub)' * C * r where: C is a 3 x 3 rotation matrix: [ cos θ cos ψ, -cos Φ sin ψ + sin Φ sin θ cos ψ, sin Φ sin ψ + cos Φ sin θ cos ψ] [ cos θ sin ψ, cos Φ cos ψ + sin Φ sin θ sin...

Homework Statement After having struggled yesterday with this as much as I could, I am posting this problem here- if ##ax+bsec(tan^{-1}x)=c## and ##ay+bsec(tan^{-1}y)=c##, then prove that ##\frac{x+y}{1-xy}=\frac{2ac}{a^2-c^2}##.Homework EquationsThe Attempt at a Solution My attempt-...

what does the period of a wave , in trigonometry ... depend on ? does it depend on the ratio of the length of the sides of the right angled triangle like this ? does it depend on the angle ?? what are all the values you need to plot a graph like this ? ??

(the x , after the sin is the representation of angle in theta) and it also means ( opposite side length/ hypotenuse side length ) how are these things related ? i mean the angle in theta , the opposite side length / hypotenuse side length ... ??

Homework Statement What is ##cos(\frac{2\pi}{7})+cos(\frac{4\pi}{7})+cos(\frac{6\pi}{7})## ? Homework Equations Trigonometry The Attempt at a Solution [/B] I remember that the answer is ##-\frac{1}{2}## But, I don't know how to do it since the angle is not nice. Any hint?

i was trying to learn some trigonometry from some basics ... after understanding terms like , f(x) = sin x , and y = sin x ... i was also getting sort of comfortable with the notations of functions ... i was also wondering , where to improve from here ... ? any good books , sites ...

Homework Statement If 1/2<=x<=1 , then cos-1[ x/2 + (√(3-3x2))/2] + cos-1 x is equal to? Homework EquationsThe Attempt at a Solution Substituting x=cosθ = cos-1(cosθ) + cos-1 [ cos(θ)/2 + (√(3(1-cos2(θ)))/2] = θ + cos-1 [cos (π/3) cos θ + sin (π/3) sinθ] =...

Homework Statement If ##cos^3x+\frac{1}{cos^3x} = 0##, then sin 2x equals ... A. -1 B. -√3 C. -√2 D. 1 E. 2 Homework Equations Basic trigonometry The Attempt at a Solution [/B] Let y = cos^3 x y+1/y = 0 y^2 + 1 = 0 y = √(-1) Then, I don't know what to do.. Help please..

Homework Statement Two identical conducting balls, b1 and b2, each with a mass of 25.0g both are hanging at 50.0cm at an angle of 45Degrees from the vertical each. Homework Equations Fg = mg Fe = kq/r^2 Ft = ? The Attempt at a Solution I made a free body diagram and am confused on what to do...

Hello. I am a sophomore and I attend an Early College High school. I am currently in Geometry this year and I will be taking Algebra II during the first half of summer. To account for the second half-credit of Algebra II, I will be taking College Algebra in the second half of summer. Throughout...

Homework Statement sin^2x + 4sinx +4 / sinx + 2 = sinx +2 Homework EquationsThe Attempt at a Solution L.S = sin^2x + 4sinx +4 / sinx + 2 =1-cos^2+4(sinx + 1) / sinx +2 Not sure where to go from there. Not sure if I was even supposed to factor out the 4?

Homework Statement ##tanx=\frac{(1+tan1)(1+tan2)-2}{(1-tan1)(1-tan2)-2}## find x Homework Equations 3. The Attempt at a Solution [/B] I tried multiplying through the paranthesis and arrived at ##tanx=\frac{(tan1tan2-1)+(tan2+tan1)}{(tan1tan2-1)-(tan2+tan1)}## and i don't know if this is any...

Can you use any trigonometric wave to describe a phenomenon between two different objects? In the sense like a line or parabola would talk about a relation between two variable thanks so much in advance

Hi all! I'm Ray and I'm new to this community, it's a pleasure! I'm trying to resolve a trigonometry exercise where I have to calculate the trigonometry Identities of a right triangle but in the specifications they don't show me any common data (hypotenuse or cathethus values), they just leave...

In a triangle whose sides are 3,4 and root 38 metres respectively, prove that the largest angle is greater than 120° My answer: Here angle C > B...(1) and C > A ...(2) adding (1) and (2) we get 2c > A+B, taking sine both side , sin2C = sin(A+B) = sin(C), therefore cosc > (1/2) therefore...

A portion of a roller coaster track is to built in the shape of a sinusoid. You have been hired to calculate the lengths of the horizontal and vertical timber supports to be used. The high and low points on the track are separated by 50 meters horizontally and by 30 meters vertically. The low...

For the given triangle as below: I can obtain trigonometry identities as below: ##\sin α = \frac{y}{r} = \cos (90° - α)## ##\cos α = \frac{x}{r} = \sin (90° - α)## ##\tan α = \frac{y}{x} = \cot (90° - α)## ##\cot α = \frac{x}{y} = \tan (90° - α)## ##\sec α = \frac{r}{x} = \csc (90° - α)##...

Homework Statement Go to the following web site: http://www.astro.utoronto.ca/~cclement/cat/listngc.html This is the portal to a large on-line catalog of variable stars in globular clusters. Each link is a cluster name and will take you to a simple text page that lists near the top the...

Hello everyone. I'm learning Trigonometry right now with myself and at current about how to find the trigonometric ratio of the angle (90° + θ) in terms of θ. I'm quite confused in the Figure. How sin(90° + θ) become equal to sin (90° - θ) of triangle P'OM'. I know that triangle P'OM' and POM...

Homework Statement What is the value of ## \frac{1}{cos^2 10^{\circ}}+\frac{1}{cos^2 20^{\circ}}+\frac{1}{cos^2 40^{\circ}}-\frac{1}{cos^2 45^{\circ}} ## ? A. 1 B. 5 C. 10 D. 15 E. 20 Homework Equations cos^2 x + sin^2 x = 1 sin 2x = 2 sin x cos x cos 2x = cos^2 x-sin^2 x The Attempt at a...

Homework Statement The anti-derivative of ∫##\frac{sinx}{sin^2x+4cos^2x}## is ##\frac{1}{\sqrt{3}}tan^{-1}((\frac{1}{\sqrt{3}})g(x))+C## then ##g(x)## is equal to : a. ##secx## b. ##tanx## c. ##sinx## d. ##cosx## Homework Equations ##d(cosx)=-sinx dx## The Attempt at a Solution I tried...

So last semester, I withdrew from Physics with algebra and trigonometry. I am currently enrolled with another professor and I hope I excel this time in the course. He seems more attentive and friendly, along with having a noticeable passion for Physics. Today was the first day of class and...

I am currently in my last year of community college before I transfer to University. Physics held me back! For my major, I am required to enroll in Physics with College Algebra and Trigonometry I & II! I took the initiative to withdraw after completing the second exam because it was extremely...

Homework Statement The truss supports a sign board as shown in the figure. Calculate the reactions at A and the force in the member FG produced by the horizontal wind load of 60lb per vertical foot of a sign. Homework Equations ΣFx=0 ΣFy=0 ΣM=0 The Attempt at a Solution Everything is right...

Homework Statement Solve for the forces P and N acting on an object in equilibrium on an inclined plane. Weight=10N, angle is 30 degrees http://blob:https%3A//www.physicsforums.com/d431a152-5681-411b-ba57-809320539165 Homework Equations Trigonometry, i.e. sin, cos, tan rules. The 'Z' rule...

I've started community college after being out of school for a while. I started with Algebra 1, Algebra 2, and Geometry: I have a strong grasp on all three. The next class offered at my school is Precalculus. Trig is not offered. The PreCalc course description "An intensive preparation for...

Homework Statement cos(x - 3p/2) = - 4/5 p <x< p/2 sin(x/2)*cos(5p/4)= ? Homework Equations The Attempt at a Solution I made it as far as to determine that sinx= 4/5 and cosx = - 3/5 but can't seems to progress any further. I am looking for an easier way to find the solution without having to...

Hey there, I will be taking calculus 2 this spring semester and I would like to know what topics from calc 1 I should be reviewing, I did receive a B+. I am also aware that trig is highly involved and my trig skills are not that good, so if there's anything from trig that is mandatory to review...

Homework Statement Given the differential equation (\sin x)y'' + xy' + (x - \frac{1}{2})y = 0 a) Determine all the regular singular points of the equation b) Determine the indicial equation corresponding to each regular point c) Determine the form of the two linearly independent solutions...

Hey I need a second opinion to see if my formulas and calculations are correct. Also I need help with graphing this problem. My problem is to find amplitude, period, horizontal shift, vertical translation, step and then graph of: y= 2 - (1/3) cos ( πx + (3π/2) ) , -1/4 ≤ x ≤ 15/4 Using the...

Find $$x$$ such that $$\tan x=1+\sqrt2$$ and $$0<x<\dfrac{\pi}{2}$$.

Homework Statement Find the value of: lim x approaches 0 of : (3x - sin 3x) / (x2 sin x) Homework Equations Trigonometry identity Limit properties No L'hopital rule The Attempt at a Solution I tried changing sin 3x to -4sin3x + 3 sin x but then I stuck. Is changing sin 3x correct way to...