Trigonometric functions (both geometric and circular), relationships between lengths and angles in triangles, and other topics relating to measuring triangles.

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1answer
22 views

Calculating tan to power -1

I have an equation of the form $$ a = tan^{-1}(y/x) $$ is this the same as $$ a = 1/(tan(y/x)) $$ It has been over 20 years since doing math and I cannot find any answers on google.
1
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0answers
17 views

Is it possible to derive circumference from these two points?

I have two points along one axis, call it y. I don't have the x axis coordinate because the points were taken as 1-D measurements. The angle between the points is known. Is it possible to derive a ...
3
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6answers
34 views

Find solutions to $\cot(x)+\csc(x)=\sqrt3$ in range $[0,2\pi]$

What is the best way to do the above? Are there any tricks I should be aware of. I know how to simplify it to $\dfrac{\cos(x)}{\sin(x)} + \dfrac{1}{\sin(x)} = \sqrt{3}$ so multiplying both sides by ...
-2
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3answers
62 views

4sin²θ + 1 = 6sinθ [on hold]

Use your graphing calculator to find the solutions to the following equations for $0° ≤ \theta < 360°$ by defining the left side and right side of the equation as functions and then finding the ...
2
votes
3answers
54 views

How to integrate $\int \cos^2(3x)dx$

$$\int \cos^2(3x)dx$$ The answer according to my instructor is: $${1 + \cos(6x) \over 2} + C$$ But my book says that: $$\int \cos^2(ax)dx = {x \over 2} + {\sin(2ax) \over 4a} + C$$ I'm not really ...
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1answer
54 views

Prove the inequality, $\root3\of4\sin^2(x/2)<3(\sin x+1-x)^{2/3}$

Prove that $$\left(\sin^2{\frac{x}{2}}\right) \cdot \frac{\sqrt[3]{4}}{3} \cdot \frac{1}{{(\sin x + 1 - x})^{\frac{2}{3}}} <1$$
3
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2answers
48 views

Is $\sin^4 x-\cos^4 x = \cos2x$ or is it $-\cos2x=\cos2x$?

A test question I received and got wrong stated that $$\sin^4x-\cos^4x = \cos2x$$ After solving the equation from lower powers of tragicomic functions it came out ...
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0answers
13 views

Position offsets from player's original position and angle in degrees. Trigonometry required.

Since I do not know how to explain exactly what I want too well, I'll just show you what I have that works and ask the question I have. ...
3
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1answer
50 views

Hard question in simple trigonometry

This question is from S.L.LONEY- If $\tan(45°+\frac{y}{2})=\tan^3(45°+\frac{x}{2})$, prove that $\frac{\sin y}{\sin x}=\frac{3+\sin^2x}{1+3\sin^2x}$. I don't know what to do. I am getting nasty ...
0
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1answer
28 views

How to approximate Heaviside function by polynomial

I have a Heaviside smooth function that defined as $$H_{\epsilon}=\frac {1}{2} [1+\frac {2}{\pi} \arctan(\frac {x}{\epsilon})]$$ I want to use polynominal to approximate the Heaviside function. ...
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0answers
28 views

Using axis coordination to represent rotation matrix instead of angles

Euler angles give us clear matrix for conversion of a vector from car reference $Fr^C$ to earth reference $Fr^E$. If $\vec V$ is a vector in different frames it is represented differently: $$\vec ...
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2answers
20 views

Differential Equations: Recursive Functions

Functions I have some familiarity with look so, $y^\prime(x) = \tan(x+2)$: straightforward expression of the first derivative of y as a function of x. But say I have a function, $y^\prime(x) = ...
2
votes
4answers
552 views

How can we know what cos(-75) is?

We need to prove it using the sum and difference formula. We also need to use special triangles. how? I've tried doing cos(a-b) but I did cos(-30)cos(-75)
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2answers
20 views

cos (arc csc (x+3)/4)

Write the expression as an equivalent algebraic expression involving only x. (Assume x is positive.) Here is my work: (arc csc((x+3)/4) let theta = arcsin 4/(x+3) sintheta = 4/(x+3) Then I made a ...
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2answers
15 views

If sin A = −3/5 with A in QIII, find sec (A/2)

1) For the following, assume that all the given angles are in simplest form, so that if A is in QIV you may assume that 270° < A < 360°. If sin A = −3/5 with A in QIII, find sec (A/2) Can ...
2
votes
2answers
57 views

Confusion with seeming lack of notational coherence between $\sin^{-1}(x)$ and $\sin^2(x)$

It seems that $\sin^2(x)$ is used to denote the square of whatever value $\sin(x)$ is, instead of the expected $(\sin(x))^2$. Based on that, I would assume that $\sin^{-1}(x) = \frac{1}{\sin(x)}$, ...
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3answers
44 views

Calculate trigonometric $ \sin(2\arcsin\frac{12}{13}) $ [on hold]

I need to calculate the following trigonometric expression without a calculator: $ \sin(2\arcsin\frac{12}{13}) $
4
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5answers
44 views

Factorising trigonometric functions

In order to factorise $x^2-1$ one way of thinking about it would be to set it equal to zero and solve to get $x=1$ and $x=-1$. You can then write $x^2-1=(x+1)(x-1)$ Can we do the same with ...
2
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3answers
65 views

What are “tan” and “atan”?

As the title says, I'm confused on what tan and atan are. I'm writing a program in Java and I came across these two mathematical functions. I know tan stands for tangent but if possible could someone ...
0
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1answer
16 views

Probability function of Acos(x)

Let's say I have a signal $y(t) = Acos(2\pi f_c t)$, where $f_c$ is the carrier frequency and $t$ is the independent variable. Since I work with discrete signals i sample this signal with a sampling ...
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1answer
17 views

Finding the volume of the following solid using triple integrals

Find the volume of the solid in the first octant bounded by the coordinate planes, the cylinder $x^2 +y^2 =4$ and the plane $z+y=3$. I found the integral bounds just fine. So I have $\int_{0}^{2} ...
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3answers
61 views

How to solve $x=\arctan(\tan(-8))$?

How to solve $x=\arctan(\tan(-8))$? My instinct would just be to say $x=-8$ but I think that there is some restrictions with domains of $\tan(x)$ any help?
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2answers
51 views

integrating sine raised to fraction

Not super math-y myself, but writing a small script for an algorithm where sine is raised to the power of a fraction. Found lots of examples for sine raised to 1, 2, 3, and ways to solve for this, but ...
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1answer
38 views

Constructibility of $\arctan\left(\frac{1}{2}\right)$

I would like to show that $\arctan\left(\frac{1}{2}\right)$ is not a constructible number. I would like to use the following lemma: Let $P(x)=x^3+ax^2+bx+c$ a polynomial with ...
2
votes
2answers
34 views

what is the lowest point of a tilted elliptical plate?

I'd like to know the lowest point $z_\min$ of an ellipse with radius $r_x, r_y$ in (Euclidian) XY that's tilted in XYZ - first rotated around X axis by $\gamma$, then rotated around Y axis by ...
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3answers
35 views

Help solve for length $PQ$

how do I approach this question using simultaneous equations with trig and or pythag??? Solve for length $PQ$ Cheers bob
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0answers
22 views

How to approximate a trigonometric to make less computation complexity

I having a trigonometric function such as $$ p_2(s) = \begin{cases} \frac {1}{(2 \pi)^2}(1-\cos (2 \pi s)), & \text{if $s \le1$ } \\ \frac {1}{2 }(s-1)^2, & \text{if $s >1$ } ...
0
votes
7answers
103 views

Evaluate the limit $\lim\limits_{ x \to 0} \frac {\sin 5 x } {\sin 2 x }$

$$\quad\quad \lim_{ x \to 0} \frac {\sin 5 x } {\sin 2 x } $$ I don't know how to start, should I multiply by something... to simplify the expression or ...?
2
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3answers
25 views

Investigating the bijectivity of $ 2 x + |\cos(x)| $.

The question asks if the function $$ f(x) = 2 x + |\cos(x)| $$ if (one-one, onto), (many-one, onto) or (one-one, into). After a long process of plotting the graph, I managed to guess it’s one-one and ...
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0answers
14 views

Sine and cosine graph transformation

I'm having some difficulties with this question A bike is on a stand such that the highest point of the back wheel is 47 inches above the ground. If the pedal is turned counter clockwise, the back ...
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4answers
20 views

Finding the exact values of trig functions in a quadrant

I need some help solving some questions because I have no idea how to solve them, and some explanation would be appreciated. The questions says: Given $\cot\alpha=\frac{\sqrt{13}}{6}$ and $\alpha$ ...
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1answer
37 views

Triangles and law of sine, cosine question [on hold]

Im having problems with this question and I've tried lots of approaches yet keep getting the similar or a close answer to what im getting an its always wrong
3
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0answers
33 views

Triangles, sine and cosine problem

Hi everyone I tried solving this countless times but I always get the wrong answer! what I did first is 600/tan(46) - 600/tan(40) and that sounded reasonable to find the answer! but I keep getting it ...
0
votes
2answers
50 views

Simultaneous Trigonometry Question [on hold]

I have the following two equations: $$17\,t\cos\theta = x + 8\,t\sin\alpha,$$ $$17\,t\sin\theta = y + 8\,t\sin\alpha.$$ [Note: $x$, $y$ and $\alpha$ are the only known values. $\theta$ and $t$ are ...
4
votes
1answer
44 views

Using trigonometry to predict future position

Intro I'm currently creating an AI for a robot whose aim is to shoot another robot. All I want to do is to be able to calculate at what angle to shoot my bullet, so that it hits my enemy, with the ...
1
vote
1answer
28 views

3D Trigonometry Problems [on hold]

I need help with solving this problem. I just don't know how to approach it. If I had another side, I could solve it using Sine Law, otherwise, I'm not sure... It's number 49 I need help with. ...
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0answers
25 views

find the corect angle to cut pipe

I have pipe penitrating a wall at an angle shooting up. I have to attach a 90 degree ellbow an drop from 90 plumb,so I will have to cut the unlevel pipe on an angle to achive a plumb drop from 90. How ...
2
votes
2answers
48 views

How to smoothly approximate a sign function

I have a function that defined as following $$f(x) = \begin{cases} 1, & \text{if $x > 0$ } \\ 0, & \text{if $x=0$ } \\ -1, & \text{if $x<0$ } \end{cases}$$ In practice, the $f(x)$ ...
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votes
2answers
66 views

How do I calculate the following limit? [duplicate]

$$\lim_{h\to 0}\frac{\sin(x+h)-\sin(x)}{h}$$ Using the fact that: $$\lim_{x\to 0}\frac{\sin(x)}{x}=1.$$ Thank you in advance for any help.
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0answers
33 views
+50

How to determine when this two variable transformation is invertible?

I am given: $$ X= U \cos(V) \tag{1}\\ $$ $$ Y = U \sin V \tag{2}$$ Now, I need to: a) Give the respective ranges for $U$ and $V$ in order that the transformation defined is one to one. and ...
3
votes
5answers
176 views

Evaluating trigonometric limit.

Evaluate $\lim_{x \to 0} \cfrac{ x\tan 2x - 2x \tan x}{(1-\cos 2x)^2} $ This is what I've tried yet: $$\begin{align} & \cfrac{x(\tan 2x - 2\tan x)}{4\sin^4 x} \\ ...
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2answers
26 views

Basic law of cosine problem

Question: In triangle ABC, if $a = 120$ cm, $b = 66$ cm, and $C = 120^\circ$, find $c$. Applying the law of cosine: $$c^2 = (120)^2 + (66)^2 - (2\cdot120\cdot66\cdot\cos120^\circ)$$ $$c^2 = 14400 + ...
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0answers
12 views

Why do I get these remarkable wave patterns when I put in the sine of (the coefficient of except 0) for x: y=sin((coefficient barring zero)x)

I saw this inequality grapher on Math Is Fun and when I was playing around with it one time, I got something so remarkable: when you enter the sine of (coefficient barring zero)x, it gives you a wave ...
1
vote
2answers
30 views

Computing $\arctan x$ in terms of a certain collection of other functions

I know that $$\tan(x) = \frac{\sin(x)}{\cos(x)}.$$ Does this relationship hold in the inverse in any form? For example: atan(x) = asin(x) / acos(x), or atan(x) = acos(x) / asin(x), or atan(x) = ...
-2
votes
1answer
21 views

Find the matrix A of “T” in the basis B [on hold]

Let V ={asin(x) + bcos(x)| a,b element of R} with ordered basis B = (sin(x), cos(x)). Let @: V->V be defined by @(V)= d(v)/dx (differentiation). Find the matrix A of @ in the basis B. Please help. ...
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2answers
43 views

Linear algebra - Find the determinant of [on hold]

Without computing the determinant, show that: I know this involves using the sin angle formula but I cant figure out how to show this without computing the determinant
0
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4answers
34 views

Trignometry, Unable to solve this .. [on hold]

Prove that .. $$2\sec\theta=\frac{\tan(90-\theta)}{\csc\theta+1}+\frac{\csc\theta+1}{\cot \theta}$$
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vote
2answers
39 views

Find the value of the following series.

The expression $\tan\theta+2\tan(2\theta)+2^2\tan(2^2\theta)+\dots+2^{14}\tan(2^{14}\theta)+2^{15}\cot(2^{15}\theta)$ equals to : The answer in the answer book is given to be $\cot\theta$. I am ...
1
vote
4answers
32 views

Find Solution of trigonometric complex equation

Find the solutions of $\sin z = 3$ There are 2 ways to solve this, I know how to do this with: $\sin z = \frac{1}{2i}(e^{iz}-e^{-iz}) = 3$ Now, I am now doing in the way: $\sin z = \sin x \cosh y+i ...
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0answers
10 views

Proving that equilateral triangle has equal medians. [on hold]

How to prove that equilateral traingle has equal medians? Mathematical method. Thank you. :D