# Tagged Questions

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### Trigonometric Identity Problem - Cos Tan and Sin

I have been going through my lecture notes for a structures question (the solution of a 2nd order ode for a buckling problem) when I came across a very weird trigonometric simplification which I just ...
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### How to find area of triangle from its medians

The length of three medians of a triangle are $9$,$12$ and $15$cm.The area (in sq. cm) of the triangle is a) $48$ b) $144$ c) $24$ d) $72$ I don't want whole solution just give me the hint how ...
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### How does a calculator calculate the sine, cosine ,tangent using just a number?

Sine Θ = oposite/hypotenuse Cosine Θ = adjacent/hypotenuse Tangent Θ = oposite/adjacent So in order to calculate the Sine or the cosine or the tangent I need to ...
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### Right-angled isosceles triangles

If a right-angled triangle is isosceles then the other two angles must be equal to $45^\circ$ ? Is this always the case or are there other possible right-angled isosceles triangles?
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### Find next point in ellipse given the chord length

I would like to draw a cloud programmatically. For this reason I need to know where to draw the next circle around the ellipse. Given the chord (circle radius), how can I calculate the next point in ...
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### $\pi$ is just a number, or also the circumference of a sub-unit circle?

A unit circle defined in the Cartesian plane has a radius of $1$ and a diameter of $2$. So making a full round is $2 \pi$. Now, $\pi$ is the ratio of the circumference over the diameter, so if I have ...
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### Trigonometry Word Problem--Not sure if correct

From point $A$ the angle of elevation to the top of a newly constructed building is $17.2$ deg. From point $B$ which is $153$ meters closer to the building the angle of elevation at the top of the ...
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### Force required to push an object?

What is the force required to push a 1000 lb object up a ramp that is inclined at a 40 degree angle?
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### Why do these trig functions “overpower” each other?

For example, $\sin(x)\cos(x)$ can be written as $\sin(2x)/2$, the limit as $x$ approaches $0$ of $\sin(x)\cos(x)$ is $0$, and the limit as x approaches $\pi/2$ is $0$. I don't see a reason why sine ...
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### Circular motion trig

We have $x_P = -2 + 4 \cos (-\pi t)$ and $y_P = 1 + 4 \sin ( - \pi t)$ with $t$ in seconds. We have to find the coordinates of the intersection with the y-axis. So I use trig and I eventually end up ...
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### Can you find the resultant force between these two vectors?

Determine the magnitude of the resultant force on an object if force $A$ is pulling the object with $150$ lbs of force and force $B$ is pulling with $300$ lbs, and the angle between the two forces is ...
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### Find the value of $\tan^2\alpha+\cot^2\beta$

A circle with centre o have two chords AC and BD,which are intersecting each other at P.If $\angle AOB=15^\circ$ and $\angle APB=30^\circ$,then find out value of $$\tan^2\angle APB+\cot^2\angle COD$$ ...
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### Find the angle between the 2 points (50.573,-210.265) and (117.833,-80.550)

I am attempting to find the angle between the 2 points (50.573,-210.265) and (117.833,-80.550). Is my calculation correct because a program is giving me a different answer? It says the angle is ...
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### Find the value of $\frac{\tan\theta}{1-\cot\theta}+\frac{\cot\theta}{1-\tan\theta}$ [duplicate]

I want to know an objective approach to solve these type of expression in a quick time Which of the expression equals to $$\dfrac{\tan\theta}{1-\cot\theta}+\dfrac{\cot\theta}{1-\tan\theta}$$ ...
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### Definite integration of a trigonometric function

How to integrate $$\int_0^{\pi/2}\!\dfrac{2a \sin^2 x}{a^2 \sin^2 x +b^2 \cos^2 x}\,dx$$ my first step is $$\frac{2}{a} \int_0^{\pi/2}\!\dfrac{a^2 \sin^2 x}{a^2 +(b^2 - a^2) \cos^2 x}\, dx$$ I ...
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### $\sum_{n=1}^\infty(n\ \text{arccot}\ n-1)$

Is it possible to calculate the following infinite sum in a closed form? If yes, please point me to the right direction. $$\sum_{n=1}^\infty(n\ \text{arccot}\ n-1)$$
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### Find the equation of the hyperbola given foci and the minor axis

first time posting and using the site. I have a quick problem that I need some help with. I need to find the equation of a hyperbola given the foci and the length of the minor axis. The foci ...
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### What's the difference between arccos(x) and sec(x)

My question might sound dumb, but I don't really see why the graphics of arccos(x) and sec(x) are different, because as far as I know arccos is the inverse cosine function (cos(x)^-1) and sec equals ...
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### A trigonometric identity for special angles

Prove that for a natural number $n$, $$\prod_{k=1}^n \tan\left(\frac{k\pi}{2n+1}\right) = 2^n \prod_{k=1}^n \sin\left(\frac{k\pi}{2n+1}\right)=\sqrt{2n+1}.$$
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### How do you integrate the following trigonometric function involving sin and cos?

How do you integrate the following functions: $$\int \left( \frac{\cos\theta}{1+\sin^2\theta} \right)^2 \, d\theta$$ and $$\int \left( \frac{\cos\theta}{1+\sin^2\theta} \right)^3 \, d\theta$$ ...
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### Help me solve a trigonometric equation

I am doing some work in RF circuit design. I need to solve an equation for my design: $$\frac 1{\cos(t_1)}+\frac 1{\sin(t_1)} =\frac 1{\cos(t_2)}+\frac 1{\sin(t_2)}$$ (I created a nicely typed image ...
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### Trigonometry Addition Thereom With Only one exact value?

Use the expression of $\sin(A+B)$ to evaluate $\sin 195$. Do I use one exact value like $45+150$ or $60$ or is there another way?
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Using the expansion of a. $\sin(𝐴+𝐵)$, prove that $\sin75°=\sqrt 6+\sqrt{24}$ b. $\sin(𝐴+𝐵)$, prove that $\tan75°=2+\sqrt 3$ Where to start? draw up triangle of sin 75? find other values? help ...
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### Trigonometric equality $x = 99 \sin (\pi x)$

Find the number of real solutions of $\displaystyle x = 99 \sin (\pi x)$. I am getting stuck in some trigonometric relations.
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### $\int_0^\infty\text{Ci}(x)^3\mathrm dx$

Is there a closed form for this integral: $$\int_0^\infty\text{Ci}(x)^3\mathrm dx,$$ where $\text{Ci}(x)=-\int_x^\infty\frac{\cos z}{z}\mathrm dz$ is the cosine integral?