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

learn more… | top users | synonyms (1)

1
vote
1answer
32 views

The graph of tan(sec(x))

A lot of the trig_function(trig_function(x)) look something like this, with asymptotes that have infinite (?) oscillating (?) lines infinitely approaching them ...
-1
votes
2answers
63 views

How to Calculate csc(2.85) in Calculator?

In my calculator (TI-84), there are only $sin, cos,$ and $tan$ commands (and inverse sin, inverse cos, inverse tan). I had a question that was as follows: Calculate $csc(2.85)$ in which I was ...
2
votes
1answer
57 views

How we can find the sign for trigonometric functions without graph

For $\sin(x)$ or $\cos(x)$ etc. how we can show that it is negative on $\left[\pi ,2\pi \right]$ ? without graph? So if we have $\sin(2x)$ or $\cos(2x)$ how we can find the sign on $\left[0,2\pi ...
1
vote
3answers
53 views

Integral of a tangent function

$$ \displaystyle {\int_{0}^{z}} \sqrt {1 + \tan^2(\dfrac{\pi}{4} \dfrac{z}{H} )} dz $$ _ $$ gives $$ _ $$ \dfrac{4H}{\pi} {\sinh^{-1}} ( {\tan \dfrac{\pi}{4} \dfrac{z}{H} } ) $$ Please advise ...
1
vote
1answer
44 views

Infinite summation of a trigonometric series

$\sum_{n=1}^{n=\infty}\sin(\frac{n\pi x}{L})\sin(\frac{n\pi y}{L})\surd(k^2+\frac{n^2 \pi^2}{L^2})$ I am trying to solve the above summation. I still could not figure out if this summation converges ...
0
votes
1answer
44 views

Finding speed of snowballs given initial velocity and angles

You and a friend stand on a snow-covered roof. You both throw snowballs from an elevation of $14$ m with the same initial speed of $12$ m/s, but in different directions. You throw your snowball ...
1
vote
1answer
12 views

How can I find the inner limit of a line passing through a lune?

I have a crescent defined by two offset circles with different radii: a small one (let's call it outer circle) centered at (0,0) with radius ...
1
vote
2answers
53 views

Is $\log_{\cos x}(1)$ defined at $x=0+2k\pi$? [duplicate]

I have an equation like this: $\cos(x) ^ {\sin(x)} = 1$ I thought I would solve it like this: $\cos(x) ^ {\sin(x)} = 1$ $\sin(x) = \log_{\cos(x)}(1)$ $\sin(x) = 0 $ $x = 0+k\pi$ But I'm ...
10
votes
3answers
496 views

In a 30-60 right triangle the side opposite the 30 degree angle is half the length of the hypotenuse. Why?

In a 30-60 right triangle the side opposite the 30 degree angle is half the length of the hypotenuse. A statement from the trigonometry section of Simmons' Precalculus in a nutshell. Please ...
2
votes
2answers
67 views

Volume of a parallelepiped, given 8 vertices

Given the eight vertices $(0,0,0)$, $(3,0,0)$, $(0,5,1)$, $(3,5,1)$, $(2,0,5)$, $(5,0,5)$, $(2,5,6)$, and $(5,5,6)$, find the volume of the parallelepiped. I'm having trouble finding the 1 vertex ...
-2
votes
2answers
58 views

$\int _{k\pi }^{\left(k+1\right)\pi }\:\left|\sin\left(x\right)\right|dx$ [closed]

How can I solve the following integral? $\int _{k\pi }^{\left(k+1\right)\pi }\:\left|\sin\left(x\right)\right|dx$
2
votes
2answers
44 views

Proving the Derivative of cosine and sine functions

In the proof of the derivatives of cosine and sine functions, we used the facts that: $$\lim\limits_{\Delta x \to 0} \frac{\cos \Delta x - 1}{\Delta x} = 0$$ and $$\lim\limits_{\Delta x \to 0} ...
0
votes
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
395 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
68 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
33 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
21 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
44 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
votes
1answer
50 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
91 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
39 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
36 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
votes
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
votes
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
vote
3answers
50 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
42 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?
-2
votes
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
votes
2answers
33 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?
1
vote
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
421 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
37 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
vote
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
votes
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
16 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
35 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
42 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
19 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
12 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.