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

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0answers
30 views

(sin10+sin50+sin130)/sin80 = ? Solution please [closed]

$\frac{\sin10+\sin50+\sin130}{\sin80}$= ? Solution please, Thanks in advance
0
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0answers
21 views

Invert an Excel function containing the tangent

In the following excel formula: =95*1*1/TAN(RADIANS(M3-(10.3/2.01)))/5280) $M3=2.63715$ and let's say the result of this formula is: $5.508306483$ What would ...
8
votes
5answers
380 views

How to construct a line with a given equal distance from 3 Points in 3 Dimensions?

Important: I'm now convinced that 4 points are needes in order to reduce the solutions to a finite number. (Which is necessary because I need ALL solutions) In a computer science context I need to ...
0
votes
1answer
30 views

Requirements for learning and understanding trigonometry?

Im reaching a point in programing where I need to create basic shapes which I simply cant since my math skills are very bad. After finding out that the skills required are trigonometry I read a few ...
3
votes
1answer
68 views

Evaluating: $I_1 = \sin^{-1} \left(\sqrt{\frac{x}{x+a}}\;\right) $

$$I_1 =\int \sin^{-1} \left(\sqrt{\frac{x}{x+a}}\;\right) dx= ?$$ I tried substitution: $\sin^{-1} \left(\sqrt{\frac{x}{x+a}}\;\right) = \Xi$, but then I'm not able to do anything after the resulting ...
-2
votes
2answers
23 views

to find the value of angle A in the given equation

4 sin A cos A = 1 - 2 sin A + 2 cos A I could not find the value of either sin A or cos A in the above equation. So please direct me on how to find the values of ...
2
votes
2answers
67 views

Squeeze Theorem: $\lim_{x\to 0} \, \frac{x^2}{\sin ^2(x)}$

I'm having a hell of a time understanding how to apply the Squeeze Theorem and the corresponding theorems to solving problems like the following. $\lim_{x\to 0} \, \frac{x^2}{\sin ^2(x)}$ So I can ...
0
votes
1answer
32 views

Given $\tan x +\cot x = 3$ and $x$ is in first quadrant. Find $\sin x$.

Simplifying, I have $$\frac{1}{\sin x\cdot \cos x} = 3$$ I have tried many manipulations but did not get the answer. Point me the right direction to the solution. (This problem is in the beginning ...
0
votes
0answers
17 views

Parallelogram with vertices 0, Xa, Xb, Xa+Xb (X is matrix, a and b are vectors)

There is a paralellogram with vertices 0, a, b, and a+b, whose area is $34$. What is the area of the parallelogram which has vertices 0, Xa, Xb, and Xa+ Xb, where X = \begin{pmatrix} 3 & -5 \\ -1 ...
1
vote
1answer
42 views

Sine Sum : Inverse Circular Function Proof

It is known that the following holds good: $$ \sin^{-1} x + \sin^{-1}y \\ \begin{align} &=\sin^{-1}( x\sqrt{1-y^2} + y\sqrt{1-x^2}) \;\;;x^2+y^2 \le 1 \;\text{ or }\; x^2+y^2 > 1, xy< 0\\ ...
-5
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1answer
48 views

How to Prove this mathematical expression???? [closed]

We know x isn't equal ninety degree . How to prove this ????????? $$ 1/\cot^6x - 3\tan^2x/\cos^2x = 1 + \tan^6x $$ Please describes step by step. Thanks.
5
votes
1answer
89 views

Find the value of $\sum_{m=1}^\infty tan ^ {-1}\frac{2m}{m^4+m^2+2}$

How to find value of this sum? $$\sum\limits_{m=1}^\infty \tan^{-1}\left(\frac{2m}{m^4+m^2+2}\right)$$ I can't understand how to simplify this. Should I use any trigonometric substitution to simplify ...
0
votes
0answers
37 views

How to draw regular tetrahedron from center?

How to calculate all four points of regular tetrahedron if you have x,y and z for center point and x, y and z axis rotation and size of tetrahedron? I want to write this in java script and this is ...
2
votes
3answers
52 views

Determine height/width of rectangle in perspective

I have the following situation. I've got a 2d plane in which I have drawn a rectangle (red). This is done by picking a point (big red dot), and using the vanishing points calculated by some other ...
0
votes
2answers
31 views

Trisecting a line in the complex plane

We have $x = 11-13i$ and $y = 35-i$. $a$ is a complex number which trisects the line segment joining $x$ and $y$. $a$ is also closer to $x$ than $y$. Find $a$. I'm not sure where to start. Would a ...
0
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1answer
19 views

Get angle in degrees of coordinate on circle.

So assume I have coordinates of two points on a circle, and the coordinate of the center of the circle. How would I go about finding the angle of the points in degrees?
4
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3answers
364 views

Approximation of the Sine function near $0$

What is the reason that for $x<0.5$, $\sin(x)\approx x$? Are there more known properties of these kind for other trigonometry functions?
1
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3answers
48 views

Proving algebraic equations with circle theorems

I got as far as stating that OBP=90˚ (as angle between tangent and radius is always 90˚), and thus CBO=90˚- 2x. CBO=OCB as they are bases in a isosceles. COB=180-90-2x-90-2x. But after this, i am ...
1
vote
0answers
41 views

Prove that these result are the same

I did this trigonometric integral in two different ways, and the results that I got were with two different trigonometric functions, $\sec x$ and $\tan x$. The integral is: $\mathbf{\int tan^{5}x \, ...
-1
votes
1answer
26 views

The asymptote of $y=\mathrm{sinc}(t)$ as time increases

Is there any known approximate formula that maps decay percentage of $\mathrm{sinc}(t)$ with decaying time? Or in other words, is there a known asymptote of $y=\mathrm{sinc}(t)$ as time increases?
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1answer
30 views

Calculate the area between functions

[I need to find the area between this three functions, therefore I need to use Integral g(x)-f(x) but I tried and it gives me negative and enormous numbers.]
-2
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2answers
32 views

very simple trig question.

I'll leave out the full story of how I got here, but basically, there is a right triangle with angles of $69$ and $21$ degrees and a base of length $6$. How do I find the side lengths?
0
votes
2answers
31 views

Highschool Geometry: Finding Common Tangent

I can't seem to identify what the arrows are indicating in this question, obviously the two lines are parallel but what does it mean? I don't know where to begin. Any suggestions?
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0answers
34 views

Confused about integration over zeroes.

Does for example $\int_{-\pi}^{\pi} \sin(x) \, dx$ cancel out to zero (following WolframAlpha/normal integration technique), or do we have to take the absolute value of all the areas between bounds ...
0
votes
2answers
30 views

An identity involving the Chebyshev polynomials

Let $n \in \{0, 1, 2, \dots\}$ and let $T_n$ denote the Chebyshev polynomial of degree $n$: $T_n(x) = \cos\left(n \arccos(x)\right)$. Let $t_0, t_1, \dots, t_n$ be $T_{n + 1}$'s roots: $t_i = ...
4
votes
3answers
419 views

Finding the exact value of arctan function then adding it?

The question is $x = \arctan\frac 23 + \arctan\frac 12$. What is $\tan(x)$? I'm having trouble figuring out how to calculate the arctan values without a calculator, or do I not even need to find ...
-1
votes
2answers
36 views

$y=3^{\cos(x)}$ how to graph this goniometric function

Please help me with graphing this function $y=3^{\cos(x)}$ without grapher. Thanks in advance for all your procedures.
1
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0answers
22 views

Can you always cover a circle in a finite number of steps with this “radar” algorithm?

Suppose you have a disc $C$ of radius $V$ with center $c$ and you randomly place a point $p$ in it. $p$ Behaves as follows: at every time-step, $p$ calculates its angle to $c$, and moves a distance of ...
0
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0answers
29 views

Trying to Find Bounds on a Trig Function

I have the function $|\sin(\frac{N+1}{2}x)\sin\frac{Nx}{2}|$ and I want to use inequalities to get it to the form $c\sin\frac{Nx}{2}$ for some constant $c$. For a little perspective, I am going to ...
0
votes
1answer
15 views

Find triangle angle knowing side length change and angle change

There is triangle A with angle $\alpha=x$ and adjacent size $a$, and triangle B with angle $\beta=x-20$ and adjacent size $b=2a$, so \begin{align*} cos(x)/cos(x-20)=1/2 \\ \end{align*} How do I find ...
-1
votes
4answers
48 views

how to solve $\sin\theta+\sqrt{3}\cos\theta=-\sqrt{3}\;$ for $\;\theta\;$ when $\;0^\circ\leq\theta<360^\circ$ [closed]

I need to solve the below equation for $\theta\;$ if $\;0^\circ\leq \theta< 360^\circ$: $$\sin\theta + \sqrt{3} \cos \theta = -\sqrt{3}$$
2
votes
0answers
48 views

Is this integral is right or wrong?

We did this exercise in class in a way, but at home I tried to solve it in a different way and I do not know if it is right or wrong. May you help me please? $\mathbf{\int tan^{5}x \, \, \, sec^{4}x ...
0
votes
3answers
34 views

If $\triangle ABC\;,\frac{a}{b}=2+\sqrt{3}$ and $\angle C=60^0,$ Then find ordered pairs $\left(\angle A,\angle B\right)$

In a $\displaystyle \triangle ABC\;,\frac{a}{b}=2+\sqrt{3}$ and $\angle C=60^0,$ Then find the ordered pairs $\left(\angle A,\angle B\right)=$ $\bf{Options}::$ $(i)\; ...
0
votes
3answers
34 views

Establish the identity: tan u(csc u - sin u) = cos u

I'm struggling to establish the identity below: $$\tan\,u(\csc\,u - \sin\,u) = \cos\,u$$ I've ended up with: $${1 - 2\sin\,u \over \cos\,u}$$ I don't know if this is correct so far, and if it is, ...
-1
votes
3answers
41 views

Evaluate the indicated trigonometric function

Question states: Assume that theta is an acute angle in a right triangle satisfying the given conditions. Evaluate the indicated trigonometric function $\tan \theta = 1/5;$ What is $ \csc \theta$ ...
-4
votes
1answer
43 views

Prove trigonometry identity: [closed]

Prove trigonometry identity: $\frac{1+cosx}{1 -cosx} = (cscx + cotx)^2$ I have no idea what to do first to prove the left side is equal to the right side.
3
votes
3answers
49 views

Prove the following trigonometric identity

$$\frac{\tan{(\frac{\pi}{4}+x)}-\tan{(\frac{\pi}{4}-x)}}{\tan{(\frac{\pi}{4}+x)}+\tan{(\frac{\pi}{4}-x)}} = 2\sin{x}\cos{x}$$ ============== On L.H.S, I've tried to write it using the sum and ...
0
votes
1answer
17 views

Find the position of a circle tangent to two other circles

Say there are 3 circles, A, centered at point a, B centered at point b, and C, centered at point c. Each has a known radius independent of the others, Ar, Br, and Cr. The positions of a and b are ...
1
vote
1answer
11 views

Trigonometry / Sum of two angles (α + β) if sinα = 8/17 and sinβ = 15/17

Find the sum of two angles α and β if sinα = 8/17 and sinβ = 15/17 if they are A) acute B) obtuse How do you approuch this problem? I'm stuck at the begging. Please help.
0
votes
1answer
15 views

Rearrangement of harmonic oscillation formulae

Can anyone show me why the following identity is true? $$A\cos(\omega t) + B\sin(\omega t) = \sqrt{A^2+B^2}\cos\left(\omega t + \arctan\left({ \frac BA}\right)\right) $$ I ask this is relation to ...
0
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1answer
13 views

Inverse Trigonometry Plots ArcT(T(x))-Clarification

enter image description here The graphs are plots of functional forms $T^{-1}(T(x))$ where T is a trigonometric function:sine,cosine,tangent,cosecant,cotangent,and secant Can someone please ...
0
votes
2answers
36 views

How should trigonometric expressions be simplified?

I have been learning trigonometric identities and I am having trouble understanding how they should be applied to simplify expressions. For example, the expression $2\sin{x} \cos{x}$ is equal to ...
2
votes
2answers
36 views

Solving the indefinite integral of a trig function

I'd like to ask for some feedback on my calculation. Please let me know if you spot any mistakes in my technique: $$\int{\frac{1}{\sqrt{x}}\sin^{-1}{\sqrt{x}}}\,\,dx$$ Using substitution: $$u = ...
0
votes
1answer
21 views

Solving the definite integral of trig function

I'd like to ask for some feedback on my calculation. Please let me know if you think it's correct, or if I messed up somewhere: ...
0
votes
1answer
18 views

Terminals and co-terminals for angles

I'm trying to understand how my teacher converted these angles. I'm not sure if my title is correct but I'm assuming that's what he was doing. For a unit circle he had, \begin{align*} u & = ...
0
votes
0answers
35 views

Derivatives of hyperbolic functions and Osborne's rule.

I am slightly confused when it comes to Osborne's rule when you take derivatives of hyperbolic functions. For example. The derivative of cotx is -cosec^2x, so there is a product of sines. So should ...
0
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4answers
48 views

Prove a trigonometric identity [closed]

$$\frac{1}{\csc A-\cot A}-\frac{1}{\sin A} = \frac{1}{\sin A} - \frac{1}{\csc A+\cot A}$$
0
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4answers
49 views

Solving an equation with the sum of inverse cosine and inverse tangent

I have the below question and have to find value of $x$. $$ \cos^{-1}\left(\frac{x^2-1}{x^2+1}\right)+\tan^{-1}\left(\frac{2x}{x^2-1}\right) = \frac{2\pi}{3}$$ I took $x$ as $\tan y$ but it isn't ...
0
votes
0answers
16 views

How to find the Laplace Transform of two (independent) functions multiplied together?

How does one find the laplace transform for an equation consisting of two trig functions multiplied together, when it is not possible to use any trig identities? For example, take a function say; ...
2
votes
4answers
58 views

Characterization of the $x$ such that $\sin(x)$ is rational?

For $x \in [0,\pi/2]$, $\sin(x)$ ranges over $[0,1]$. So every rational number in $[0,1]$ is the sine of some $x \in [0,\pi/2]$. Q. Is there any characterization of the $x$ for which $\sin(x)$ is ...