Tagged Questions

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

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1
vote
3answers
353 views

Finding $\cos(s+t)$

I am attempting to find $\cos(s+t)$ and $\cos(s-t)$ I am given that they are in quadrant II and that $\cos s = -1/5$ and $\sin t = 3/5$. I have no idea what the relation between these numbers $s$ or ...
3
votes
3answers
1k views

Euler formula and $\sin^3$

Using the formula: $$e^{i\omega t} = \cos {\omega t} + i\sin{\omega t}$$ I would like to prove that: $$\sin^3\;x = -\frac{\sin{3x} - 3\sin{x}}{4} $$ However I haven't found any approach ...
0
votes
3answers
647 views

Finding $\csc$ with $\cot$

I know that $\cot\theta = 4/3$ how do I find $\csc\theta$? I tried to do $\csc^2\theta - \cot^2\theta = 1$ This gives me $\csc^2\theta = 1 + \cot^2\theta$ this gives $csc^2\theta = 9/9 + 16/9 = ...
0
votes
5answers
371 views

Trig test review [closed]

Well I just failed a trig test. Any help on why I did things wrong or what went wrong in my thought process? I triple checked all my answers and was positive I had 100 percent on this test, instead I ...
2
votes
1answer
45 views

determing x,y increase by angle?

If I had a position of 0,0 and I had an angle of 45 degrees (or any number) and my velocity was 1 what would be the x,y increase? For example if I had a 90 degree angle, and I had a velocity of 1. ...
5
votes
1answer
207 views

Why are these two functions equal?

These functions are equal. But I don't understand why. $$a \leftrightarrow f(x) =|\cos(2\pi x)|^2$$ $$b \leftrightarrow f(x) = \dfrac{\cos(4\pi x)}{2} + 0.5$$ Which results both in this plot:
2
votes
2answers
167 views

solving a problem using degrees OR radians

hey so i'm programming something that finds an angle of a line between 0 and 180 degrees based on two points.... the equation to find the answer is ...
6
votes
3answers
2k views

Definite integral: $\displaystyle\int^{4}_0 (16-x^2)^{\frac{3}{2}} dx$

The following integral can be computed using the substitution $x = 4\sin\theta~$ and then proceeding with $dx = 4\cos\theta~ d\theta~$, and evaluating the integral of $\cos^4\theta~$: ...
1
vote
1answer
66 views

find point of object in the future given direction and velocity

I have a point A, and another point B. I know the distance from point A to B. I also know the velocity with which B is moving and its direction. I also know the angle of B with respect to A. I would ...
1
vote
2answers
197 views

Trig identities

I need to prove that: $$1+\tan x \tan 2x = \sec 2x.$$ I started this by making sec 1/cos and using the double angle identity for that and it didn't work at all in any way ever. Not sure why I can't ...
-1
votes
1answer
130 views

Trig identities

Finally got to double angles. Anyways I need to show that these are identities. $$\sin(4x) = 4 \sin(x) \cos(x) \cos(2x)$$ The book does some magic and gets $$2(2\sin(x)\cos(x))\cos(2x)$$ This makes ...
6
votes
3answers
422 views

$\int \cos^2 x$ - Where did I go wrong?

So when looking on the question: $$\int_{0}^{\pi} \cos^2 x \ \text{d}x$$ I would just subtract $\cos^2(0)$ from $\cos^2(\pi)$, but doing so would get me 1 - 1 = 0. When the answer is $\pi/2$. Where ...
0
votes
1answer
161 views

Calculus question - Trig Identities

Alright so I've got the question: $\int2\sin^2(x)\cos^2(x)dx$ And in class I learned: $\sin^2(x) = ((1-\cos(2x))/2)$ $\cos^2(x) = ((1+\cos(2x))/2)$ So when I substitute I get: ...
0
votes
1answer
81 views

Check if a rectangle bisects another rectangle

I've seen many examples of checking for a rectangle (A) intersecting another rectangle (B), but I'm developing something where I need to check if A is bisecting (crossing outside of) B. My intersect ...
3
votes
5answers
330 views

Finding $\sin(4a)$ if we know $\cos a$

I need to show that $\sin 4a = 0$ if $\cos a = 0$. I am not sure how to do this really. I know I can take $\sin^2 x + \cos^2 x = 1$ but I don't think that helps. I was also suppose to find the ...
3
votes
0answers
202 views

Maximum size of a rotated-then-cropped rectangle

With regard to topic/question New size of a rotated-then-cropped rectangle: The answer by Isaac, the maximum area is $b^2\csc\alpha\sec\alpha$ when $x=0.5b\csc\alpha = 0.5b/\sin\alpha$ seems to ...
2
votes
1answer
163 views

Solving trigonometric equation involving summation

For $ 0 <\theta<\frac{\pi}{2}$ find the solution of $$\sum\limits_{m=1}^{6}\csc\left(\theta+\frac{(m-1)\pi}{4}\right)\cdot\csc\left(\theta+\frac{m\pi}{4}\right)=4\sqrt{2}$$ I thought of ...
-1
votes
1answer
308 views

Is there a way to reverse the effect of $a\tan2$?

I have a specific question about reversing $a\tan2$. (I am programmer, sorry for the jargon). I also use the $a\tan2$ function in my example, but I think everybody knows what it means. radial = ...
8
votes
2answers
557 views

Reduction formula for $I_{n}=\int {\cos{nx} \over \cos{x}}\rm{d}x$

What would be a simple method to compute a reduction formula for the following? $\displaystyle I_{n}=\int {\cos{nx} \over \cos{x}} \rm{d}x~$ where $n$ is a positive integer I understand that it ...
3
votes
3answers
209 views

$\frac{\pi}{2} =\tan^{-1}(\infty)$

Using the result, $\tan^2{\alpha} - A \tan{\alpha} + 1 = 0~$, where A is a constant, prove that the two solutions to this equation (such that $0 \leq \alpha \leq \frac{\pi}{2}$) are complementary ...
1
vote
3answers
360 views

Factoring trig expressions

This should be simple but I am horrible at math. Anyways I forgot basic math properties and when I try to work it out in more simple terms I can't make sense of anything. Anyways I have to factor ...
2
votes
3answers
119 views

Trig identities

I need to perform the indicated operation and simplify $(1+\sin t)^{2} + \cos^{2} t$ The book is telling me that it turns into $1 + 2\sin^2t + \cos^2t$, how is is possible? Basic math tells me that ...
1
vote
2answers
3k views

How would one calculate the cosine of an obtuse angle?

How would you calculate the cosine of an obtuse triangle's largest angle? Cos = adj/hyp. But which side is the adjacent side?
1
vote
2answers
115 views

How do I compute $2ab\cos C$ given $a,b,C$? Isn't an operator missing there?

I have an equation. For example the law of cosines, $c^2 = a^2 + b^2 - 2ab \cos C$ So I calculate it all and I get something like this: 2500 cos 130. I calculate the cos 130, and get -0.643 Now what? ...
0
votes
2answers
107 views

Touch up on Trig

I have forgotten a few things about trigonometry and angles. I have this trig equation, $\sin \theta = \frac{200\text{ dyn}}{224\text{ dyn}}$ What exactly are the steps of getting the angle, ...
10
votes
2answers
794 views

Algebraic proof of a trig matrix identity?

I'll put the question first, and then the background, because I'm not sure that the background is necessary to answer the question: I have a geometric proof, but is there an elegant algebraic proof ...
0
votes
3answers
173 views

Graphing trig functions

I tried to continue my homework but ran into another problem I couldn't do, literally can't continue now. I have to graph $\displaystyle y=\frac 32 \sin2\left(x+ \frac{\pi}{4}\right)$ What do I do ...
0
votes
1answer
113 views

Graphing sin, finding phase shift, period and transformations

I need to graph $$y=2 \cos\left(x - \frac{\pi}{3}\right)$$ and I am having trouble figuring out what points will be on the graph. The book tells me to split it into four parts, which doesn't make ...
3
votes
2answers
71 views

Graphing cos and transformations

I need to graph $y=-2\cos3x$ I just went the standard route and reflected across the x axis, multiplied the y axis by 2 and multiplied the x axis by three. Is this incorrect? I got the wrong answer ...
15
votes
7answers
1k views

Proving $\frac{1}{\sin^{2}\frac{\pi}{14}} + \frac{1}{\sin^{2}\frac{3\pi}{14}} + \frac{1}{\sin^{2}\frac{5\pi}{14}} = 24$

How do I show that: $$\frac{1}{\sin^{2}\frac{\pi}{14}} + \frac{1}{\sin^{2}\frac{3\pi}{14}} + \frac{1}{\sin^{2}\frac{5\pi}{14}} = 24$$ This is actually problem B $4371$ given at this link. Looks like ...
4
votes
4answers
339 views

$\tan(\frac{\pi}{2}) = \infty~$?

Evaluate $\displaystyle \int^{\pi}_{0} \frac{dx}{5 + 4\cos{x}}$ by using the substitution $t = \tan{\frac{x}{2}}$ For the question above, by changing variables, the integral can be rewritten as ...
3
votes
1answer
440 views

dot product negative angle

I have two two-dimensional unit vectors a and b. I'm trying to get their angle related to their order. arc cosine of the dot ...
13
votes
4answers
7k views

What is the length of a sine wave from $0$ to $2\pi$?

What is the length of a sine wave from $0$ to $2\pi$? Physically I would plot $$y=\sin(x),\quad 0\le x\le {2\pi}$$ and measure line length. I think part of the answer is to integrate this: $$ ...
0
votes
1answer
692 views

The unit circle and circular functions

I am attempting to do my homework but my book got lost in the mail, I have a test on Monday, and I only have the homework problems and my meticulous notes from class. The next set of homework asks ...
3
votes
1answer
64 views

How do I find a point $(x_1,y_1)$ if I have an origin point $(x_0,y_0)$, a distance, and $\theta$?

I'm trying to figure this out for player movement in a video game but I'm having trouble figuring it out: How do I find a point $(x_1,y_1)$ if I have an origin point $(x_0,y_0)$, a distance, and ...
0
votes
4answers
338 views

tan=sec? test questions

If $\theta$ is in quadrant 1 and $\tan(\theta) = .6$ then $\sec(\theta) = $? This seems pretty easy to me: $\tan^2(\theta)-\sec^2(\theta)=1$ $-\sec^2(\theta)=.64$ $\sec(\theta)=8$ Another one, ...
-3
votes
1answer
881 views

Exact Values for sine of integer angles

I have the exact values for the sine of integers. Has this been accomplished before? Jim Parent
13
votes
2answers
567 views

Machin's formula and cousins

There exists a well-known formula by John Machin: $$\frac{\pi}{4} = 4 \arctan \frac{1}{5} - \arctan \frac{1}{239}.$$ Actually, it belongs to the family of Machin-like formulas of the form ...
3
votes
2answers
410 views

Diffraction and Computer Generated Holography Calculations

I've tried this through Mathematica, and hit my own limit in math ability trying to do this, both to no avail. I'm assuming there is no way to do so, as a simple solution to this problem would be a ...
2
votes
3answers
6k views

Integral of $\sqrt{1+\tan^2x}$ [duplicate]

Possible Duplicate: Ways to evaluate $\int \sec \theta d \theta$ I'm having a bit of a problem with an integral. The original problem was the length of a curve given parametrically. I've ...
0
votes
4answers
104 views

solving triangles

I have $\displaystyle\frac{56.851}{\tan(42.0892^\circ)}$, how do I figure that out on a calculator? I tried and I keep getting syntax error and I don't know how to make degrees. Google was no help ...
2
votes
1answer
222 views

How can I see alternative trigonometry solutions on a calculator?

When doing inverse trigonometric equations on a calculator, only the lowest positive solution is shown. How can I see alternative solutions (specifically for a Casio FX85ES)? Current behaviour: ...
1
vote
1answer
305 views

expression for Dirichlet's kernel like sum

It is given in the book that the Dirichlet's kernel $D_n(t) = 1/2 + \sum\limits_{k=1}^{n} \cos(kt)$ is given as $\frac{\sin(n+1/2)t}{2\sin(t/2)}$. I'd like to know if there is any such expression for ...
0
votes
1answer
161 views

Reference angles

How do I find reference angles? Using this as a reference http://www.howe-two.com/mathematicat/reference.html I don't understand why in the first example it moves positive and then in the second it ...
4
votes
1answer
331 views

Get polar equation from cartesian equation

I have this equation: $x^4 + y^4 = x^2 + y^2$ and I need to convert it to a polar one... I have tried and the result is $$r = \sqrt{\frac{1}{\cos^4\theta + \sin^4\theta}}$$ Is this ok?
0
votes
2answers
182 views

solving $\sec (3 \beta + 10) = \csc (\beta + 8)$

$\sec (3 \beta + 10) = \csc (\beta + 8)$ (in degrees) I am supposed to find one solution, and the angles are acute. I do not know the answer or how to get the answer. It is confusing for me ...
-2
votes
2answers
285 views

Finding exact values for trig functions

Finding exact values for trig functions of acute angles. I have $\sin \theta = 3/5$. I know that $y = 3$ and $r = 5$. How the heck do I get $x$ if I don't know the angle?
-4
votes
1answer
220 views

Finding two sides of a triangle [duplicate]

Possible Duplicate: calculate sides of the right triangle if I know 1 side and all the angles I'm not sure how to do this with only 1 side given, but I have a right triangle with a 30 ...
5
votes
6answers
394 views

Can you explain $(1 + iX/n)^{n}$ without using e, sin, or cos?

In my ongoing strugle to understand $e^{\pi i}$ I managed to narrow down my conceptual difficulty. I'm having intuitive trouble understanding why $(1 + iX/n)^{n}$ is conceptually the same as a ...
-3
votes
4answers
783 views

Angle equations

I have no idea what to do at all for this question, we just learned trig values and I don't see what to do for this question. I think it has something to do with co functions (as in cosine, cotan, ...