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

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2answers
21 views

Why is that for any trigonometric function $f, f(2\pi + \theta )=f(\theta )$ for any value of $\theta$ [proof reading]

Here was the question asked to me :: Why is that for any trigonometric function $f, f(2\pi + \theta )=f(\theta )$ for any value of $\theta$ I spontaneously said that it was because of their very ...
0
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0answers
10 views

The instantaneous value of current, i amp, at t seconds is given by: i = 15 sin(100π.t + 0.6) so…find the value of…

The instantaneous value of current, i amp, at t seconds is given by: i=15sin(100πt+0.6) Find the value of; The amplitude The period The frequency The initial phase angle (when t=0), expressed in ...
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1answer
16 views

Finding the velocity of an object from its horizontal and vertical components?

Let's say a ball is thrown and it experiences typical projectile motion (moves in a parabolic arc etc.) and the only information we know are the equations for the horizontal and vertical components of ...
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1answer
10 views

Show P, Q and R are non collinear

If P $\equiv$ $(-sin(\beta - \alpha), -cos\beta)$, Q $\equiv$ $(cos(\beta - \alpha), sin\beta)$ and R $\equiv$ $(cos(\beta - \alpha + \theta), sin(\beta - \theta))$, where $$0 \lt \alpha, \beta, ...
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2answers
40 views

Trig:What's the graph of $\,\,\sin x .\sin x$?

I've been googling the graph of $\,\,\sin x .\sin x$ to see a visual of a trig problem i'm working on: $\sin^2x=\frac 14$ intervals $0$ to $2 \pi$. you have to use this equation to solve: ...
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5answers
50 views

Limits without L'Hopitals Rule

Evaluate the limit without using L'hopital's rule a)$$\lim_{x \to 0} \frac {(1+2x)^{1/3}-1}{x} $$ I got the answer as limit = 2/3... but I used L'hopitals rule for that... How can I do it another ...
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2answers
36 views

Why is the unit circle the preferred circle to derive values of trig functions?

I am reviewing basic trigonometry and came across a nice example that uses an equilateral triangle (sides of length r), cut in half vertically, to demonstrate that cos(60) = r/x = r/(r/2) = 1/2. From ...
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1answer
27 views

How is $r(\theta) = \sin \frac\theta2$ symmetric about the x-axis?

I understand how it is symmetric about the $y$-axis. because $r(-\theta) = \sin \left(-\frac\theta2\right)=-\sin \left(\frac\theta2\right)=-r(\theta)$ But how is it symmetric about $x$-axis?
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2answers
17 views

find the cosine of the angle ABC

I have problem with solving this task. I know that the answer might be A. But only with calculator by calculating the angles. can someone explain me or give me a hint to solve it. cos^-1 (5/13) = ...
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1answer
27 views

Limits and Trigonometry (Squeeze Theorem) [on hold]

So the question states to use the Squeeze Theorem to evaluate the following limits. (a) $\lim\limits_{x \to 1}\quad (x-1)\sin \left(\frac{\pi}{x-1}\right)$ (b) $\lim\limits_{x\to 0^-}\quad x^3 ...
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1answer
17 views

Explain trigonometry rewrite

While looking at a solution to a longer task I found this part that confuses me. How is this rewrite done? As it is presented in a one step way it should be trivial but I can't see it. $$ \left| \sin ...
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4answers
115 views

How can I prove this question concerning trigonometry? [on hold]

Prove that, for some constant $B$, $$4\cos(x) - 3\sin(x) = 5\cos(x+B).$$ Then, estimate the value of $B$.
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0answers
9 views

Simultaneously solving trigonometric equations

Let $N\in\mathbb N$. Given $\theta_1,\ldots, \theta_N\in [0,2\pi)$ I would like to prove that there exist $\rho\in\mathbb R_+$ and $\varphi\in[0,2\pi)$ such that $$ f_\ell(\rho,\varphi):=\theta_\ell ...
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4answers
83 views

$\text{Prove that}$ $\frac{\sin(\frac{n+1}2)*\cos(\frac n2)}{\sin\frac 12} \ge\frac n2$

Prove that$$\frac{\sin\left(\frac{n+1}2\right)\times\cos\left(\frac n2\right)}{\sin\left(\frac 12\right)} \ge\frac n2$$ So far I've switched up the problem and gotten it down to all sin functions. I ...
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2answers
11 views

Partial derivative of trig function

I need some assistance on the following calculus problem: Let $$w = 2\cot(x)+y^2z^2$$ $$x = uv$$ $$y = \sin(uv)$$ $$z = e^u$$ Find $\frac{\partial w}{\partial u}$ for $u = \frac{1}{4}$ and $v = ...
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2answers
39 views

How do you solve this trig/geometry question?

In a quadrilateral $ABCD$, if $\sin\left(\frac{A+B}2\right)\cos\left(\frac{A-B}2\right) + \sin\left(\frac{C+D}2\right)\cos\left(\frac{C-D}2\right) = 2$ then $\sin\left(\frac A 2\right) ...
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1answer
44 views

Prove this trigonometric identity? [on hold]

Prove that $(\tan^2 \theta -\sin^2 \theta) = (\tan^2 \theta) \cdot (\sin^2 \theta)$
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2answers
29 views

How to write $a^{ix}$ in terms of $\sin(x)$ and $\cos(x)$?

We know that $e^{ix} = \cos(x) + i\sin(x)$ and the plot of $2^{ix}$ seems to have sinusoidal behavior. http://goo.gl/Xfg2wp Can we claim that we can write $a^{ix}$ in terms of $\sin(x)$ and ...
2
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3answers
36 views

Proving that $\dfrac{\tan(x+y)-\tan x}{1+\tan(x+y)\tan x}=\tan y$

Edit: got it, silly mistakes :) I need to prove that $\dfrac{\tan(x+y)-\tan x}{1+\tan(x+y)\tan x}=\tan y$ $$=\frac{\tan x+\tan y-\tan x+\tan^2x\tan y}{1-\tan x\tan y+\tan^2x+\tan x\tan y}$$ ...
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1answer
59 views

Fermat's Last Equation

Sorry this is an amateur question but I was wondering since Andrew Wiles solved Fermat's Last Theorem what effect does this have any impact on Geometry. Does this prove in a sense Higher Order right ...
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1answer
16 views

Calculating quadrant facing from a rotational matrix and two 3d vectors

I am working on a space-ship simulator, and having trouble with facing arcs between two space objects. Each object has a rotation matrix defined as follows: ...
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1answer
21 views

equation for the radius of a circle that is tangent to two lines and passing through a specific point on one of the lines?

I'm interested in finding the equation for the radius (and optionally the center point) for a circle that is tangent to two lines and passing through a specific point on one of the lines. So far, I've ...
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1answer
44 views

Trying to find an $\arctan(x/y)$ identity.

I have this equation : $$\theta = \arctan\left(\tfrac xd\right) + \arctan\left(\tfrac yd\right).$$ $\theta$ is an angle and I am trying to express $d$ as a function of $\theta$. So is there a way ...
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3answers
25 views

Implicit differentiation with trig function

I have the following expression which I need to implicitly differentiate: $$ xy^2 + x^2 + y + \sin(x^2y) = 0 $$ I'm a little confused as I'm not entirely sure what to do with the trig function. ...
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1answer
34 views

Calculating the points of a annular sector type shape.

The problem involves a circle inside a square sharing a common center point. The circle is always smaller than the square so that their edges never intersect. Then an annular sector (see cyan shape in ...
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1answer
18 views

Finding the vertical shift of a sinusoidal function

I'm currently studying sinusoids, I've been given a graph with a few key points and have been told to find a cosine function which fits it. When it comes to finding the vertical shift of the graph the ...
1
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2answers
42 views

$m\cos^2{\theta} + n\sin^2{\theta} < l \implies \sqrt{m}\cos^2{\theta} + \sqrt{n}\sin^2{\theta} < \sqrt{l} $

Prove that $m\cos^2{\theta} + n\sin^2{\theta} < l \implies \sqrt{m}\cos^2{\theta} + \sqrt{n}\sin^2{\theta} < \sqrt{l} $ for every $m, n, l >0$.
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2answers
20 views

Definite integral of trig function

I'm looking for some assistance on the following problem: Let $$ T(x) = \int_{4r^3}^{4} tsin(t^3)dt $$ Find $$T'(r)$$ I'm struggling to find the antiderivative of the sine function, particularly as ...
3
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6answers
95 views

Find the first derivative $y=\sqrt\frac{1+\cosθ}{1-\cosθ}$

$$y=\sqrt\frac{1+\cosθ}{1-\cosθ}$$ my professor said that the answer is $$y'=\frac{1}{\cosθ-1}$$ she said use half angle formula but I just end up with ...
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4answers
48 views

Unable to differentiate $\cos(x) \cos(2x) \cos(3x)$ and $\sqrt{\frac{(x-1)(x-2)}{(x-3)(x-4)(x-5)}}$

I apologize for the lack of LaTeX. I will update this question with the proper LaTeX as soon as possible. I am having trouble with two differentiation exercise questions and was hoping someone could ...
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2answers
145 views

Is Pythagoras the only relation to hold between $\cos$ and $\sin$?

Pythagoras says that $\cos^2 \theta + \mathrm{sin}^2\theta = 1$ for all real $\theta$. (Vague) Question. Is this the only relationship between the functions $\cos$ and $\sin$? More precisely: Let ...
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2answers
21 views

Slight help with inverse trigonometry question

I apologize for the lack of LaTeX, i will try to learn LaTeX and update this question as soon as possible. I am having some trouble with an inverse trigonometry question and was hoping that someone ...
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0answers
20 views

simplify and find domain for triginomic function

I am just doing some review and a question requires me to simplify and find the domain of this function, $\sin(2)\sin(2x)$ how do I find the domain?
2
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1answer
34 views

Equilateral Triangle Problem With Trig

I have an Equilateral triangle with unknown side $a$. The next thing I do is to make a random point inside the triangle P. The distance $|AP|=3 cm, |BP|=4 cm, |CP|=5 cm.$ What is the area of the ...
0
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0answers
15 views

Bounds on sum of sines/angles.

I have the following equalities: $$ \sin(\theta) + b_x = sin(\theta_a) \\ \cos(\phi) + b_y = cos(\phi_a) $$ My goal is to find upper bounds for the following: $|\theta - \theta_a|$, $|\theta + ...
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0answers
36 views

Trigonometry problem - No right angles triangle [on hold]

I got a trigo problem I need to solve asap :p I've got a triangle, with no right angle. 1 of the side length is know, and the opposite angle is known too. I am spliting the triangle with a line ...
0
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0answers
39 views

How to determine $\cos(a) = \frac{4}{6}$? [on hold]

So I know that $\cos(a) = \frac{4}{6}$ Now I need to determine $\cos\left(\frac{13\pi}{2}\right)+a$ and provide its exact value, but I don't know how to determine $a$ since $\frac{4}{6}$ is not in ...
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1answer
33 views

Constructing triangle using side length-median relationship

$$\begin{align} m^2_a&=\frac{2b^2+2c^2−a^2}4\\[4pt] m^2_b&=\frac{2c^2+2a^2−b^2}4\\[4pt] m^2_c&=\frac{2a^2+2b^2−c^2}4 \end{align}$$ Solving for $a$, $b$, $c$ in terms of $m^2_a$, $m^2_b$, ...
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1answer
41 views

Desmos.com simulating spinning orbital object

https://www.youtube.com/watch?v=U_VsPV1WJbg As shown in the video, the face with the eyes and mouth are orbiting an unplotted circle with radius = 4, but also spinning (rotating) in a circular motion ...
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0answers
37 views

How to find the components of a vector, given magnitude and angle?

Problem The velocity of an aeroplane is $100$ km/h at an angle $30$ degree from north toward west. Draw a vector diagram to obtain its north and east components. Progress The work I already tried ...
3
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1answer
67 views

Question of trigonometry

If $\cos^2 A=\dfrac{a^2-1}{3}$ and $\tan^2\left(\dfrac{A}{2}\right)=\tan^{2/3} B$. Then find $\cos^{2/3}B+\sin^{2/3}B $. I tried componendo and dividendo to write the second statement as cos A but ...
2
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1answer
33 views

Proving $\left(\frac{1+\sin x+i\cos x}{1+\sin x-i\cos x}\right)^n=\cos n\left(\frac{\pi }{2}-x\right)+i\sin n\left(\frac{\pi }{2-x}\right)$

How to solve the following question? If $n$ is an integer, show that \begin{eqnarray} \left(\frac{1+\sin x+i\cos x}{1+\sin x-i\cos x}\right)^n=\cos n\left(\frac{\pi }{2}-x\right)+i\sin ...
0
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1answer
63 views

Prove $\sin(x)< x$ when $x>0$ using LMVT

According to Lagrange's Mean Value Theorem (LMVT), if a function $f(x)$ is continuous on $\left[a,b\right]$ and differentiable on $\left(a,b\right)$, then there exists some constant $c$ such that ...
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votes
2answers
81 views

Trig Equation - 2 years out of math & lost [on hold]

$$\cos^2(2x) + \sin^4(x) = 2$$ So lost on how to solve these things and it's already midnight. 3 days I've spent reviewing and doing practice, but I can't find any proper information on how to go ...
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1answer
15 views

Math question about solutions on intervals in trig. [on hold]

Find all solutions in the interval $[0, 2 \pi)$ for $$ 2 \cos x \csc x - 4 \cos x - \csc x + 2 = 0 \,? $$
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1answer
111 views

What is the value of $\csc^2\frac{\pi}{14}+\csc^2\frac{3\pi}{14}+\csc^2\frac{5\pi}{14}$? [duplicate]

How to compute $$S=\csc^2\frac{\pi}{14}+\csc^2\frac{3\pi}{14}+\csc^2\frac{5\pi}{14}$$ I tried to rewrite it in terms of $\sin$ $$ ...
0
votes
2answers
30 views

Non-trigonometric Continuous Periodic Functions

I've seen lots of examples of periodic functions, but they all have one thing in common: They all involve at least one trigonometric term (e.g. $\sin\theta$, $\cos\theta$, etc.). My question is ...
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1answer
26 views

If α, β are two values of θ satisfying equation cosθ/a + sinθ/b = 1/c then prove that cot ((α+β)/2) = b/a

What I did was $$b\ \cos (\theta) + a \sin (\theta) = \dfrac{ab}{c} \\ b\ \cos (\theta) = \frac{ab}{c} - a\ \sin (\theta) $$ Square both sides and using sum of roots and product of roots as ...
-2
votes
2answers
41 views

If xsinθ = ysin(θ + 2π/3) = zsin(θ + 4π/3) then prove that Σxy = 0?

Please help! I don't know how to solve this question. I tried putting the whole thing equal to "k" and then calculating values of x,y and z in terms of k and putting there. But it messes up the ...
1
vote
1answer
58 views

Why do both trig functions have the same Macluarin series?

Both the degree version and the radian version of the trig functions have the same Maclaurin series, yet they are different. How is this possible? How can two different functions have the same ...