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
22 views

Calculate angle betwen two lines

I have been trying to find the best solution to this problem, but my math is pretty bad. What I want to do is calculate the "Angle" in radians, I have all the 3 co-ordinates and all the 3 lengths ...
0
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0answers
19 views

Basis of Trigonmetric Polynomials Help

Write the following trigonometric polynomials in terms of the basis functions: $\cos^2(x)$ $\cos^2(x) \sin^3(x)$ Is there a certain way to solve these types of problems because I'm very unsure on ...
0
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0answers
3 views

finding the phase of a signal - solving a non-linear (trigonometric) system of equations

I'm trying to calculate the phase2 value in the y2 equation of a signal given a specific frequency if I know the other values. Is this possible? Example below: ...
2
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2answers
51 views

Is it possible to expand $\sin(2x+1)\cdot\sin(2x+1)$?

Is it possible to treat it as a binomial?
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3answers
18 views

Finding an angle $\theta$ in a complex number

If we know that $z = \frac{1}{\sqrt2}(\cos\theta+i\cdot\sin\theta)$ and also that $z = \frac{(\sqrt3-1)+i(\sqrt3+1)}{4}$ How can I find $\cos\theta$ and $\sin\theta$? Using a calculator it gives me ...
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2answers
22 views

Trig Identity Confusion

Solving a problem I came across $\cos^2(t) - \sin^2(t) + 1$. The back of the book has the next step answer as $\cos(2t) -1$. Using the double angle identity how is it possible to receive the $-1$?
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2answers
15 views

Am I going about this wrong? Complex expression to polar form

I have the expression below, which I'd like to write in polar form. $$z = \frac{i}{{1+\frac{i(\sqrt3-1)}{1+i}}}$$ Own process My process was very tedious; and I also wouldn't solve the final part ...
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votes
1answer
35 views

De Moivre's Theorem for proving

I have been asked by my lecturer to answer this question but I'm having problems doing so. The question is: Prove that $$\cos (5\theta) = 16\cos^5\theta - 20\cos^3\theta + 5 ...
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0answers
24 views

Condition for trigonometric inequality

I want to prove the following statement: Suppose $\frac{1}{4}(\cos(\theta_1)+\cos(\theta_2))^2+\lambda^2(a\sin(\theta_1)+b\sin(\theta_2))^2\leq 1$ holds for all $\theta_1,\theta_2\in[-\pi,\pi]$, then ...
0
votes
2answers
43 views

Why is the sine and cosine always between $-1$ and $1$?

Why is the sine and cosine always between $-1$ and $1$? If I would have circle with a radius other than $1$, then it wouldn't be between $-1$ and $1$ anymore, would it? This also ties in with another ...
2
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5answers
42 views

Proof of $\arcsin x \le 2\arctan x$?

I am looking for a proof for the following 'fact': $$ \arcsin x \le 2\arctan x \quad \forall x\in[0,1). $$ I put fact between single quotes, as the only proof I found is a plot by wolframalpha. I know ...
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1answer
14 views

Using sine law determine missing angel x

Okay so I need to use SINE to determine the missing angle. (X). I know one angle is 85 degrees. And the sides are 25mm, 43.8 mm, and 36 mm, can someone please tell me what I have to put into my ...
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vote
2answers
50 views

How is $\tan^{-1}(a/b) = \tan^{-1}(a) - \tan^{-1}(b)$?

I'm having a problem proving: $\tan^{-1}(a/b) = \tan^{-1}(a) - \tan^{-1}(b)$ Thanks!
1
vote
3answers
58 views

The value of $\int_0^{2\pi}\cos^{2n}(x)$ and its limit as $n\to\infty$

Calculate $I_{n}=\int\limits_{0}^{2\pi} \cos^{2n}(x)\,{\rm d}x$ and show that $\lim_{n\rightarrow \infty} I_{n}=0$ Should I separate $\cos^{2n}$ or I should try express it in Fourier series?
0
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0answers
21 views

Calculating originally arc approximated by cubic bezier curve

I have an cubic bezier curve, which is representing an arc by an approximation. The approximation was calculated with the kappa constant: $$ \\k = \frac43*(\sqrt{2}-1) $$ This means, that the ...
0
votes
3answers
14 views

Cyclic quadrilaterals - finding the size of an angle

I know this might seem like a really simple question, but I really don't understand where I am going wrong. I am familiar with cyclic quadrilaterals as well as their properties, but this question ...
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votes
1answer
22 views

Finding Y coordinate of third triangle point when X coordinate and two other points are already known

Suppose you know the coordinates for points A and B of a triangle. We can refer to those coordinates as (Ay,Ax) and (By,Bx). Also, suppose you know the X coordinate for point C (Cx) but do not know ...
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1answer
9 views

Find all of the exact solutions of the equation and then list those solutions which are in the interval [0, 2pi)

This is for trigonometric equations and inequalities: Find all of the exact solutions of the equation and then list those solutions which are in the interval [0, 2pi) Cos(9x)=9
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1answer
18 views

Finding Trig Functions

I am given $$\cos(\beta) = \frac{\sqrt{15}}{8}$$ and I am asked to find the indicated trig function of $$\sin(90^{\circ}- \beta)$$ I know $$\sin(\beta)= \frac{7}{8}$$ but I don't know how to go about ...
0
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0answers
17 views

The cosine rule, Bearings [on hold]

two forest rangers leave base and travel to different parts of the forest. Simone averages 70km/hr along a straight track in a direction 25 degrees, While bruce averages 80km/hr in a direction 135 ...
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votes
2answers
26 views

Limit as x approaches 0 from the left: $\lim_{x \to 0^{-}} \sin^{-1}\left({\frac{1}{2+e^\frac{1}{x}}}\right)$

Help me find the limit as x approaches 0 from the left: $$\lim_{x \to 0^{-}} \sin^{-1}\left({\frac{1}{2+e^\frac{1}{x}}}\right)$$ Thanks,
3
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2answers
52 views

Prove $\lim_{x\rightarrow 0}\cos (x)=1$ with the epsilon-delta definition of limits

Prove $$ \lim_{x\rightarrow 0}\cos (x)=1 $$ with the epsilon-delta definition of limits
2
votes
1answer
44 views

Moving a point around a circle

we're currently working on a game which involves a character that rotates around a point. We are using a rotation matrix to rotate a given a point (x,y) around another point by first translating to ...
2
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0answers
13 views

How to compute uniformly distributed points on an ellipse

The ellipse can be parametrized in polar coordinates by $$r(\theta)=\frac{1}{a+\cos\theta}$$ up to a scaling factor, and $a>1$. Suppose we measure $S$, the distance along the ellipse from the ...
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1answer
21 views

Trigonometric problem with $\cos{\alpha}$ and $\sin{\alpha}$

The problem is $$3 \cos{\alpha} = 3 - 2\sin{\alpha}.$$ Find the value of angle alpha I have some trouble solving this. I don't know where to start.
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0answers
1 views

Taking components of a system containing multiple vectors.

Q. In the arrangement shown in fig. the ends P and Q of an inextensible string move downwards with uniform speed u. Pulleys A and B are fixed. The mass M moves upwards with a speed. My text ...
-3
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1answer
31 views

If $y = 2\sin(x)-\sin^2(x)$ and $x = 2\cos(x)-\sin(x)\cos(x)$ what is $\frac {dy}{dx}$? [on hold]

If $y = 2\sin(x)-\sin^2(x)$$\ \ \ x = 2\cos(x)-\sin(x)\cos(x)$ What would $\frac {dy}{dx}$ equal to? so $\frac {dy}{dx}=2\cos(x)-\frac {2\cos(x)\sin(x)}{-2sin(x)}$ ... ? what would $y'$ of ...
0
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0answers
23 views

Determine sine wave frequency from two arbitrary points

If I have only two arbitrary points on a sine wave, what would be the simplest method for determining the frequency of the sine wave? The frequency is unknown. The bandwidth is restricted, the time ...
11
votes
2answers
120 views

How does one evaluate $\int \frac{\sin(x)}{\sin(5x)} \ dx$

The below problem is taken from Joseph Edwards book Integral Calculus for beginners. How does one show: $$5 \int \frac{\sin(x)}{\sin(5x)} \ dx= \sin\left(\frac{2\pi}{5}\right) \cdot ...
-1
votes
1answer
27 views

Is $\cos(\arctan(-x) - \arcsin(y))$ the same as $\cos(\arctan(-x)) - \cos(\arcsin(y))$?

Is $\cos(\arctan(-x) - \arcsin(y))$ the same as $\cos(\arctan(-x)) - \cos(\arcsin(y))$? Because if I put this on my calculator I got different solutions.
4
votes
1answer
37 views

How to prove this inequality relating to trigonometric function?

In a triangle, A, B, C are three corners of the triangle, try to prove that : $$\root 3 \of {1 - \sin A\sin B} + \root 3 \of {1 - \sin B\sin C} + \root 3 \of {1 - \sin C\sin A} \geqslant {3 \over ...
3
votes
4answers
48 views

$ \sin x \geq \frac{2x}{\pi}, x \in [0, \frac{\pi}{2}]$

I have tried the following: $$ f(x) = \sin x-\frac{2x}{\pi} \\ f'(x)= \cos x-\frac{2}{\pi} \\ f''(x) = -\sin x \leq 0 $$ But this doesn't seem to be heading in the right direction as it would appear ...
1
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0answers
19 views

Is a sine wave plus the sum of its odd harmonics symmetrical around the x axis at half the period of the fundamental?

I have a function such that $$x(t)=A_1 \sin(2 \pi f t+\phi_1)+A_2 \sin(2 \pi (3f) t+\phi_2)+...+ A_n \sin(2 \pi ((2n+1)f) t+\phi_n)$$ Is such a function symmetric around the point that is half ...
3
votes
3answers
46 views

Using $x=\tan \theta$ to solve $\int x\sqrt{1+x^2}\,\mathrm dx$

I'm having a lot, I repeat, a lot of trouble with Calculus II, particularly trigonometric substitution. At the moment, I'm extremely confused as to how to integrate $\int x\sqrt{1+x^2}\,\mathrm dx$ ...
4
votes
1answer
31 views

Find the missing angle of similar triangle

Find the missing angle $\theta$ in the triangle below given that $R>r$, $l\geq R$, $0< \theta < \frac{\pi}{2}$. Attempted Solution I attempted to use similar triangles to find the angle ...
6
votes
5answers
59 views

The limit as $x$ goes to infinity of $x-x\cos(4/x).$

I would like to determine $$\lim_{x\to \infty} \left(x-x\cos \frac4x\right)$$ How do I even start this? I can't plug in infinity to $4/x,$ can I? That will make it zero? Is the answer infinity then?
1
vote
2answers
40 views

How to find the exact value of $\tan(\sec^{-1} 4)$?

I would like to know if there is a general method to solve equation looking like this: $$\tan(\sec^{-1} 4)$$ without using a calculator (you have to find the exact value)? How to proceed?
0
votes
1answer
22 views

Prove this trig identity?

I'm having trouble proving the following identity: $$A\cos(\omega t) + B\sin(\omega t) = \sqrt{A^2 + B^2} \cos(\omega t - \arctan(\tfrac{B}{A}))$$ Does anyone know how this can be done? Thanks!
0
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0answers
32 views

Robotic Kinematics - Differential drive

I'm new to Kinematics and my robotic book assumes I have a base knowledge which I do not. The book doesn't do a very good job explaining for someone with minimal math background. The question is: ...
3
votes
0answers
42 views

How to evaluate the following integrals

$$\int\limits_0^{\frac{\pi }{2}} {{x^2}{{\ln }^2}\left( {\sin x} \right)\ln \left( {\cos x} \right)dx} ,\int\limits_0^{\frac{\pi }{2}} {x\ln \left( {\sin x} \right){{\ln }^2}\left( {\cos x} \right)dx} ...
2
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2answers
126 views

Need some help solving high-school level trignometry question.

here it is. I've tried solving it multiple ways but it gets too complicated. Is there any way to solve this?
0
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1answer
33 views

Trigonometry rewrite

How do you go from $$ \frac{ \sin z }{e^z -1} $$ to $$ \frac{\cos z}{e^z}$$ My first approach was to use eulers formula. But that made the calculations quite hard. I'm guessing this can be done ...
1
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2answers
46 views

Some help with sin and cos

I'm having trouble to understand the following equalities in these two equations, i.e. how to apply the addition formulas. Firstly: $$ \frac {1- \frac {sin^2(\frac x2)} {cos^2(\frac x2)}} {1+ \frac ...
0
votes
1answer
30 views

Trigonometric ratios

I'm stuck with a problem. Given is a triangle $\Delta ABC$ with $\angle A = 35°, BC=3$ and $AC=5$. I need to find the two possible values for $\angle C$. I only managed to found one angle. I did the ...
1
vote
1answer
24 views

$\tan \{\frac{1}{2} \sin^{–1} (2x/ 1 + x^2) + \frac{1}{2} \cos^{–1} (1 – y^2/1 + y^2) \}$ is equal to.

$$ \tan \left\{ \frac{1}{2} \arcsin \frac{2x}{1 + x^2} + \frac{1}{2} \arccos \frac{1 – y^2}{1 + y^2} \right\} $$ is equal to. Note: i think $\sin a=2x/1+x^2$, $\cos b=(1 – y^2/1 + y^2)$
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1answer
17 views

How many milliliters of liquid to fill [duplicate]

A right circular cone has a depth of 103 mm and a top diameter of 82.4 mm. The cone contains water to a depth of 30.0 mm. How many more millilitres of liquid need to be added in order to fill the ...
0
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0answers
95 views

Translation request: geometry problem stated in Korean [on hold]

Please im a foreing studying in south korea.. so i dont understand nothing in class... can any one tell me what is this called in english? thanks
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0answers
21 views

In need of formula: Gravity at Specific Coordinates [on hold]

Doing Research on the gravitational pull at a specific set of coordinates. Does anyone know how to solve this mathematically? Please Help. Thanks
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0answers
26 views

Find the length of the longer diagonal on a trapezium with only 2 sides stated.

Im at a loss here, i know i have to divide the trapezium, but im still not sure which calculation is relevant to it then. Thanks in advance.
1
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2answers
34 views

Trigonometry textbook or tutorial

Is there an actual textbook or online resource that has a tutorial to solve $a\sin x+b\cos x=c$ for $a, b, c$ being either positive or negative? I tried to find these types of equations/functions in ...