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

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Trigonometric manipulation

From $$\frac{R\sin(\omega t)-\omega L\cos(\omega t)}{\omega^{2}L^{2}+R^{2}}$$ I have to get $$\frac{\sin(\omega t-\alpha)}{\sqrt{R^{2}+\omega^{2}L^{2}}}$$ where $\alpha$ is a constant. How do I do ...
0
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1answer
20 views

Simple Trig Question / Introduction to Vectors Question

Sorry this is such a simple question; I'm just struggling a little with my trigonometry homework. An example question: "A ship sails due north (relative to the current) with a speed of 20 knots. The ...
0
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1answer
39 views

How does BC = sin(y)?

This is part of an exercise to work with the proofs of the sum of angles, either sin(x + y) or in this case cos(x + y). The solution steps declare BC = sin(y) without any explanation. I guessed at it ...
0
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1answer
34 views

Trig Identities [on hold]

write in terms of sine and cosine and simplify the expression $$\frac{\cos(A)-2\sin(A)\cos(A))}{\cos^2(A)}-\sin^2(A)+\sin(A)-1$$ need help solving this.
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2answers
32 views

Trigonometry question, find the value if $\cos(x) = \frac{5}{13}$ and $\cos(y) = -\frac{5}{13}$

My cousin is working on this and showed it to me. I'm unsure how to solve it. $x$ and $y$ represent two angles in standard position. $x$ has its terminal arm in the first quadrant and $y$ has its ...
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5answers
52 views

Taking the sin of arccos

When solving for the value of x in the equation $$\sin^{-1}{(\sqrt{2x})}=\cos^{-1}(\sqrt{x})$$ one would take the sin of both sides of the equation cancelling out the arcsin leaving ...
-1
votes
1answer
21 views

Proving that pressure at a point does not depend on orientation

In a) the solution states that $dS_1=$cos$\theta dS_2$, in other words it considers the surface area to be equivalent to the length of a line, in order to use basic trigonometry. I understand we are ...
0
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2answers
76 views

Fun Tan Question [duplicate]

Using only trig identities, how would you approach the following question? Determine the value of $$ \prod_{i=1}^{89} \tan i^° = \tan 1^° \cdot \tan 2^° \cdots \tan 89^° $$
2
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1answer
29 views

Ratio of sides of Triangle $ABC$

if in a Triangle $\Delta ABC$ with $a$, $b$ and $c$ as sides $$\begin{align}\left(Cot\frac{A}{2}\right)^2 ...
1
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3answers
32 views

Double Angle Trigonometry Question

So there is this question which consists of 2 parts. $$ a) \text{ Simplify } \frac{\sin2x}{1+\cos2x} \\ b) \text{ Hence, find the exact value of tan 15.} $$ So far I've discovered that $ \text{a)} ...
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0answers
15 views

Computing the coordinates of a point, offset from a rotated point.

Good day. I have a question which should be easy but I have not been able to figure it out. The coordinates of a point on a unit circle, given an angle, is $$\begin{align} x &= \cos(\alpha) \\ y ...
1
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1answer
32 views

$\tan( x + i y ) = a + ib$ then $\tan (x - iy) = a - ib $?

How to prove, if $\tan( x + i y ) = a + ib$ then $\tan (x - iy) = a - ib $ ? I am not familiar with trignometric identities. So any help will be appreciated. Thanks in Advance.
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2answers
33 views

Find the exact value of the trigonometric function $\sin 7\pi/ 6$

I am finding it a little difficult to solve this problem. The reference angle for $\sin 7\pi/6$ is sin 30 degrees (I think) which is sine 1/2. But that is not the answer. How do I sove this problem?
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0answers
14 views

Finding true bearings?

What is the true north bearing of NNE on 16 point cardinac compass? I just wanna know that is there any exact bearing or do we have to only give an approximate bearing?
1
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2answers
61 views

if $ f(x)=x+\cos x $ then find $ \int_0^\pi (f^{-1}(x))\text{dx} $?

I would be interest to show : if $ f(x)=x+\cos x $ then find $ \int_0^\pi (f^{-1}(x))\text{dx} $ ? my second question that's make me a problem is that : what is :$ f^{-1}(\pi) $ ? I would be ...
2
votes
5answers
123 views

Help me prove: sin(A+B) = sinA cosB + cosA sinB [duplicate]

Can you help me prove that: sin(A+B) = sinA cosB + cosA sinB? Thanks!
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3answers
61 views

$\arctan(-3/2)$ doesn't give expected result.

Let's say I want to find the angle measure (in degrees) such that $\tan(x) = -3/2$. It turns out that $x \approx 123.7$, and when I compute $\tan(123.7)$, I get $\approx -3/2$; so far so good. ...
1
vote
5answers
67 views

Solving $\sin x = 4\sin10°\sin40°\sin(70°-x)$

So, I have this equation: $$\sin x = 4\sin10°\sin40°\sin(70°-x)$$ And I'm trying to solve for $x$. Apparently $x=20°$ is the (smallest positive) solution but I can't arrive at it. I'm not very ...
0
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0answers
23 views

Find the relation the 'maps' 2D points to the corresponding 3D images.

I have this [on hold] question (#857264) re-phrased. Hope that the content is more meaningful now. The following is the picture modified from the original. The question is a rectangular piece of ...
6
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0answers
40 views

What transcendental numbers are produced by $\sin{\alpha}$ when $\alpha$ is algebraic/constructible/rational (in radians)?

I know that by Lindemann–Weierstrass theorem(LW) sine and cosine of non-zero algebraic numbers (in radians) produce results that are transcendental. My question is what are the transcendentals ...
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0answers
28 views

Using Algebra with Trig Functions

Using Algebra with Trig Functions I'm trying to find the correct 1 second audio signal I would need to apply to a 1 second known noise signal to have the output signal be a sin wave. The basic ...
1
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1answer
33 views

Evaluate position of first secondary maximum of $\frac{\sin N (x/2)}{\sin (x/2)}$

The function $$f(x) = \displaystyle \left | \frac{\sin \left( N \displaystyle \frac{x}{2} \right)}{\sin \left( \displaystyle \frac{x}{2} \right)} \right |$$ when evaluated for $x > 0$, has its ...
1
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1answer
23 views

Finding angle of depression?

The question is that a boy standing on the top of a staircase 33m high while looking at a oatch of grass on the ground 50 m away from him.What is the anglre from where he was looking at. Please draw ...
1
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1answer
22 views

Finding Angle of Depression

Finding angle of depression but i dont have idea that what i should mark as hyportenus or opposite? Please help!!!! So, here is the question that Chris is standing on the top of the cliff of 70 m and ...
2
votes
2answers
49 views

Trigonometry calculation problem

Problem: Calculate $\cos(\alpha+60)$, if $\sin(\alpha)=\frac{2}{3}$ and $\alpha\in[90^\circ,180^\circ]$. I have tried following: ...
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votes
1answer
21 views

Practical Trigonometry Problem [on hold]

In a right angle triangle I know the hypotenuse to be 4.7. The adjacent is 1/3 of the opposite. How do I calculate the length of the opposite? Also, what is the answer?
2
votes
2answers
112 views

Mathematical Identity

I'm stuck in a path on a paper about thermal conductivity. There is a identity involving an integral that a I can't realize how they've perfomed it. Here is it: $$\lim_{N\to \infty} ...
1
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1answer
20 views

find period of discrete cosine

let us consider following we should find period of this discrete signal,for periodicity we should have $x[n+kN]=x[n]$ or $10\cos(0.088\pi(n+kN) +\phi)=10\cos(0.088\pi n+\phi)$ or $0.088\pi ...
3
votes
5answers
80 views

How to solve $0=\cos{2x}+\cos x$

I'm desperately trying to solve $$0=\cos{2x}+\cos x$$ Am I on the right track when I'm this far? $$\cos x(2\cos x+1)=1$$ I don't know where to go from here. What method can I use to further solve ...
1
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3answers
27 views

Trigonometry - Finding value of expression

Question: Given $\sin x + \sin^2 x = 1$ then find the value of $$\cos^{12} x + 3\cos^{10} x + 3\cos^8 x + 6\cos^6 x + 2\cos^4 x + \cos^2 x -2$$ I have no idea where to start on this question. Please ...
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0answers
15 views

determine signal frequency and phase

let us consider following graph we should answer on the following question In the following figure, it is possible to measure both a positive and a negative value of $t_1$ and then calculate the ...
0
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0answers
34 views

Which Trigonometry Book is Recommended? [duplicate]

I'm taking trigonometry for this upcoming fall, and I want to get a good head start like I did with statistics a while back. I was recommended Cynthia Young' s Trigonometry book and Loney's book. ...
4
votes
3answers
104 views

all complex solutions of $z\sin(z)=1$?

A possibly easy question, Can we find all complex solutions of $z\sin(z)=1$ ? My try: Let $$\sin(z) = \frac{e^{iz} - e^{-iz}}{2i}$$ so we have $$ z\frac{e^{iz} - e^{-iz}}{2i}=1 $$ Not sure how ...
6
votes
2answers
496 views

Sum of this series

$$ \mbox{How do I find the sum of this series}\quad \sum_{n=0}^{\infty}{\sin^{3}\left(3^{n}\right) \over 3^{n}}\ {\large ?} $$ Hints in the right direction would be appreciated.
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3answers
55 views

Trigonometric Identities and formulas

There are so many identities like $\sin2θ$, $\cos2θ$, $\tan2θ$, $\sin(θ/2)$, $\cos(θ/2)$ and $\tan(θ/2)$. there are other formulas too like $\cos(α-β)$, $\sin(α-β)$ etc and yes the sum and product ...
0
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2answers
50 views

Help with circular function [on hold]

how do you graph circular function like this: (the x is a fraction.. that's my problem. :P ) $$f(x)= \frac{1}{2}\sin (x/2)$$ help me!!
0
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2answers
21 views

If $0\leq a \leq 3; 0\leq b \leq 3$ and the equation $x^2 +4+3 cos(ax+b)=2x$ has at least one solution , then find the value of a+b

Problem : If $0\leq a \leq 3; 0\leq b \leq 3$ and the equation $x^2 +4+3 cos(ax+b)=2x$ has at least one solution , then find the value of a+b. Solution : We can write the given equation : $x^2 ...
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2answers
58 views

How to solve $\sin^3 x=\sin x\,$?

$\sin^3 x=\sin x$ I have absolutely no idea what to do. I've tried graphing, and I have a little better of an understanding, but I am at a loss.
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4answers
51 views

Solving trigonometric equations to the fourth power.

$$\sin^4(x)-\sin^2(x)=0$$ My work: Let $t=\sin^2(x)$ Rewrite the original equation as: $t^2-t$ Factor: $t(t-1)$ $t=1$, $t=0$ What do I do from here?
0
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5answers
47 views

Solving a quadratic trigonometric equation?

The equation is $6 \cos^2x+\cos x=1$, My work: $6x^2+x-1=0$ $(3x-1)(2x+1)$ $3x-1=0 ∨ 2x+1=0$ $x=\frac{1}{3} ∨ x= \frac{-1}{2}$ But I do not know how to progress further.
2
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1answer
31 views

Proving that $\tan(x) = x$ has exactly one solution per interval $((n-\frac12)\pi, (n+\frac12)\pi)$

I want to prove that $\tan(x) = x$ has exactly one solution per interval $((n-\frac12)\pi, (n+\frac12))$. My attempt: $\tan(x)$ is $\pi$-harmonic, and has a range of $(-\infty, \infty)$ for each ...
2
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2answers
38 views

Solving for the principal value of a trigonometric equation

The question is as follows: $$3{\tan}^2(2x)-1=0.$$ Solve for $x$. What steps should I take to solve? The squaring is really throwing me off.
1
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1answer
22 views

Why does this get the angle of the surface?

I have this (physics) question, but am missing something as to why the math works for it. The problem is as follows: A 4- kg sphere rests on t he smooth parabolic surface. Determine the normal ...
1
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3answers
80 views

If $\cos 25^\circ + \sin 25^\circ = k,$ then what is $\cos 20^\circ$?

Question: If $$\cos 25^\circ + \sin 25^\circ = k,$$ then what is $\cos 20^\circ$? What I did: I tried to square both sides, and obtained that $\sin 50 = k^2 -1$, however, this didn't get me ...
0
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0answers
29 views

Analytical Models for Hysteresis of Complicated Systems

I’ve been working with a system that exhibits hysteresis and I’ve found that the more common models do not work for me. I am wondering if anyone is aware of other models that might be out there for ...
0
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3answers
19 views

Given three points, is the angle positive or negative?

Suppose we have the points A, B, and C on a plane. Lets say we have the line AB and AC. Is there a way to figure out if the angle between BAC is positive or negative? Ie. did we have to do a ...
2
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3answers
111 views

Evaluating a limit involving trigonometry

I really thank you for your answers to my first question--I could easily solve first problem and a few more ones without another question. But a while later I got another one while studying, then I ...
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2answers
28 views

evaluate exponential using Euler identity

let us consider following exponential $e^{-j*\pi*k/2}$ and $e^{j*\pi*k/2}$ we can decompose it as $cos(\pi*k/2)-j*sin(\pi*k/2)$ and second one same with plus sign ...
2
votes
4answers
119 views

How to solve: $\cos^2x + \sin x = 1$

$\cos^2x + \sin x = 1$ How to solve for $x$?
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3answers
24 views

Finding a point in a parallelogram

QUESTION: Find the point$(x,y)$ so that $(x,y)$ is in the first quadrant and $(x,y),(1,2),(4,10)$ and $(2,6)$ are vertices of a parallelogram.. I find this question very difficult.. Thanks...