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

learn more… | top users | synonyms (1)

-1
votes
1answer
59 views

Prove that $\cos^2\theta+\sin^2\theta=1$ [duplicate]

I try to find the question but I didn't How do you do it? I'm really stuck on this proof. Can someone please explain?
0
votes
0answers
3 views

Finding angles in Barycentric system

How to find the angles of a triangle given the barycentric coordinates of its corners? Does it work if i take the first two components of every coordinate, and find the angles in the triangle (on the ...
-2
votes
1answer
23 views

Help on Quadratic Equations [on hold]

If $\sin15$ and $\cos 15$ are the roots of a quadratic equation $x^2+ax+b=0$, then find the value of $a^4- b^2$. Please, need help, show working, thanks.
0
votes
2answers
54 views

How to solve this equation: $x+2 \tan(x)=\pi/2$

By drawing graph,or otherwise,find the number of roots of the equation $x+2 \tan(x)= \pi/2$ lying between $0$ and $2\pi$, and find the approximate value of the largest root. I found 3 roots ...
1
vote
0answers
11 views

Intersection of graphs, and no solution for trig functions.

All I know is the c=asin(x-b) I don't know how to check the values of b for 'no solutions,' in the case of trig functions. Can someone people provide an algebraic method to solve this.
2
votes
4answers
96 views

Why do you have to begin with the largest angle or side when using law of cosines

Explain why you should always start with the largest angle or the largest side when using law of cosines. I don't understand why but my professor says so.
1
vote
2answers
44 views

Fourier Transform the following exponential and cosine function: $f(x) = e^{-a^{2}x^{2}}cos(bx)$

I have a previous exam here for my course (Provided by the professor) that requires me to do a Fourier Transform of the following equation. Here is the function: $f(x) = e^{-a^{2}x^{2}}cos{(bx)}$ ...
1
vote
1answer
33 views

Solve the equation given below…

I have such an exercise: $$\color{teal}{{|x|\over{x}}\sin^2x-\cos|x|\cos x=1} $$ What I did is so: If $x\ge 0$ then we have: $$\sin^2x-\cos^2x=1$$ $$\sin^2x=1$$ So: $$\sin x=1$$ or $$\sin ...
0
votes
3answers
31 views

A trigonometric equality

Can you help me prove: $\arccos \frac{y}{\sqrt{y^2 + x}} = \mathrm{arccot} \frac{y}{\sqrt{x}}$? I could solve this problem myself, but maybe you can show me a simple way to prove this and similar ...
1
vote
2answers
32 views

Trig identity question

Show that $\sin(2nx)=\sin((2n+1)x)\cos(x)-\cos((2n+1)x)\sin(x)$. I have the mark scheme in front of me, but it doesn't make sense to me... ...
0
votes
0answers
15 views

Collision between 2d circle and flat surface

First of all I want to preface this post by saying that I am absolutely terrible at maths, my level of geometry equals being able to discern a circle from a rectangle but that's about it, as for ...
1
vote
1answer
42 views

Trig and Radians Confusion

I am learning about radians in my current class and am totally confused. How does $\sin(x+\frac\pi 2)=\cos(x)$ when $\frac\pi 2<x$ < $\pi$. I drew the triangles and I got $\sin(x+\frac\pi ...
1
vote
2answers
25 views

Find the point on an ellipse by angle.

How do I find the point on the ellipses at 45'. I found this, which answers part of it, but I need to know how to calculate for (x,y) at 45'. I could also use a good explanation for the ...
4
votes
1answer
39 views

Calculate depth using triginometry

I was asked a question like this on an exam today and I'm wondering if I got it right or not. ...
-1
votes
1answer
37 views

An error in Wikipedia? (trigonometry)

https://en.wikipedia.org/wiki/N-sphere In "Spherical coordinates" section the hyperspherical coordinates are results of arccosinus function. In some other sources there is arccotangent instead: ...
0
votes
0answers
8 views

How to find optimal perpendicular axis of rotation vector?

I am drawing lines on the screen. Each line has a point (x,y,z) and a direction (u,v,w). I want to draw arrow heads on these ...
5
votes
1answer
57 views

How to find inverse of $\sin(x) + \sin(2x) = y$?

I was wondering if there were any way to solve the equation $$\sin(x) + \sin(2x) = y$$ in terms of $x$. This of course would allow us to express the inverse for this function on $-\frac{\pi}{4}$ to ...
0
votes
0answers
24 views

Find all the angles between $0^\circ$ and $360^\circ$ which satisfy the equation.

Find all the angles between $0^\circ$ and $360^\circ$ which satisfy the equation $$\tan 3x-3 \sin 30^\circ=0$$ I tried searching for examples but didn't get any. Please teach me how to solve such ...
0
votes
1answer
33 views

Question regarding trigonometry

I've got this thing on my mind : we know that $cos(x)$ is a periodic function , hence integral from $2(k-1) \pi$ to $2k \pi$ will yield the same value for any $k \geq1$. My question is , why is ...
0
votes
1answer
23 views

Solve an Angle-Side-Angle special case triangle if it has an obtuse angle?

I've seen this type of problem multiple times on homework, and it's confusing me like mad. The scenario: We have a triangle. It is a special case triangle, with one angle, one side, and another ...
2
votes
2answers
53 views

Trigonometric substitution

Been out of touch with trigonometry for some time now. Need help proving this expression. $$\sin^{2}\left(\frac{x}{2}\right) = \frac{1}{2}(1-\cos\left(x\right))$$ Any help will be appreciated. ...
1
vote
2answers
36 views

Trigonometric equation problem

This is the following equation: $$\arccos x= \arctan x$$ Could someone give me at least a tip how to begin with?
0
votes
3answers
36 views

Solving a simple trigonometric equation $\sin x = -\sin y$

What is the solution set of the following trigonometric equation? $$\sin x = -\sin y$$
0
votes
2answers
24 views

Doubt regarding trigonometric equation

In a book of mine it says solution of $\sin^2(x) = \sin^2(y)$ is $x = n\pi \pm y$ But if we take sq root on both sides we get sinx = siny for which the solution is $x = n\pi + (-1)^ny$ Which is ...
9
votes
10answers
1k views

How to solve $4\sin \theta +3\cos \theta = 5$

Another problem that I already wasted hours on. Given $$4\sinθ +3\cosθ = 5$$ Find $$4\cosθ -3\sinθ$$ Help me guys (PS:I'm not that good in maths)
4
votes
1answer
50 views

Solving a trigonometric equation

Can someone help me to solve this problem? Find all number pairs $x,y$ that satisfy the equation: $$\tan^4(x) + \tan^4(y) + 2\cot^2(x)\cot^2(y) = 3 + \sin^2(x+y)$$
1
vote
1answer
27 views

Calculus - Trig Maximum Value Problem

When the rules of hockey were developed, Canada did not use the metric system. Thus, the distance between the goal posts was designated to be six feet. If Sidney Crosby is on the goal line, three feet ...
1
vote
2answers
39 views

Verify :$\cos^2x=\cot^2x-\frac{\cos^2x}{\tan^2x}$

$$\cos^2x=\cot^2x-\frac{\cos^2x}{\tan^2x}$$ How can I solve it?
0
votes
3answers
26 views

Sketch the graph for $0^\circ \leqslant x \leqslant 360^\circ$.

Sketch the graph $y= cos \frac{3}{4}x-2$ for $0^\circ \leqslant x \leqslant 360^\circ$. Please help me draw this. I found out that $y= cos \frac{3}{4}x-2$ has a period of ...
0
votes
1answer
23 views

Find the resulting speed and direction

A barge is pulled by two tugboats. The first tugboat is traveling at a speed of 15 knots with heading 130°, and the second tugboat is traveling at a speed of 16 knots with heading 190°. Find the ...
0
votes
2answers
23 views

Solving for x on unit circle equation

I have been given the equation $$\cos^2{x} + 2\sin{x}=2.$$ I have factored it, and the only answer I got was $x=\frac{\pi}{2}$. Is this correct or is there more than one answer? The interval is $0 ...
0
votes
1answer
21 views

Simplifying Trig Identity

I have an equation I have been given to solve, I know how to start but I do not know what to do after I use the Trig Identities. Any help? Here is what I was given $$ \frac{\cos(A + B) + \cos(A - ...
0
votes
2answers
20 views

Inequality: $\tan(x) > 1$

So far, I've not come very... far. It ends up with me trying to solve it more intuitively than mathematically. I figured, first I'll find the place of equality, which is at $x = \arctan 1 = ...
1
vote
1answer
6 views

Finding (sin(A+B))^2 given roots of a quadratic equation.

If tan A and tan B are the roots of the equation x^2 -ax + b = 0, then the value of sin(A+B)^2 is? Options are: ((a^2)/((a^2)+(1-b)^2), (a^2)/(a^2+b^2), a^2/(b+a)^2, a^2/(b^2*(1-a)^2) The value ...
4
votes
2answers
78 views

Showing $\sin{\frac{\pi}{13}} \cdot \sin{\frac{2\pi}{13}} \cdot \sin{\frac{3\pi}{13}} \cdots \sin{\frac{6\pi}{13}} = \frac{\sqrt{13}}{64}$

I would like to show that $$ \sin{\frac{\pi}{13}} \cdot \sin{\frac{2\pi}{13}} \cdot \sin{\frac{3\pi}{13}} \cdots \sin{\frac{6\pi}{13}} = \frac{\sqrt{13}}{64} $$ I've been working on this for a few ...
-1
votes
1answer
27 views

How to find coordinates of the center of circle containing a given arc [on hold]

Given: Coordinates for each end of circular arc, angle of arc, radius length. How do I find the coordinates of the center of the circle containing the arc?
0
votes
2answers
13 views

“Which is equivalent for restricted x values to”

I've been checking my homework via Wolfram Alpha, and for several questions (example below) in this section (trigonometric integrals). I'd be correct up until the last step, in which Wolfram Alpha ...
0
votes
1answer
62 views

Find the solutions of: $\sin x+\cos x=\sin^2 x+0.5\sin{2x}$

Find the solutions of: $\sin x+\cos x=\sin ^2 x+0.5\sin{(2x)}$ How can I find the solutions ?
0
votes
1answer
13 views

Law of Sine Problem

I know the law of Sine. SinA/a=SinB/b=SinC/c I think I'm missing something here... I am given ∠A=68.41°,∠B=54.23° and a=12.75ft. I found b with no trouble which is 11.119ft. I used SinA/a=SinB/b... ...
-1
votes
1answer
36 views

How to rotate a line in 3d space?

I am trying to figure out direction vectors of the arrowheads of an arrow. Basically I'm given a normalized direction vector ...
2
votes
2answers
16 views

How to find opposite and adjacent lengths of a right triangle given the hypotenuse and angle?

I'm writing a few functions for a JavaScript game engine. Is it possible to calculate the length of the legs of a right triangle given ONLY the length of the hypotenuse and an angle?
1
vote
1answer
26 views

Trigonometry - Conceptual Questions [on hold]

If anyone could help me solve these questions and provide steps, I would really appreciate it! Thanks in advance! True or False? Explain your answer. If a triangle contains an obtuse angle, then it ...
-4
votes
0answers
32 views

Trigonometry - Proofs and Derivations [on hold]

Can someone help me solve this? I need to see steps so that I can work out other homework questions just like this. I would really appreciate any help! Thanks in advance!
0
votes
1answer
21 views

Finding the value of trigonometric functions

This is probably one of the easiest concepts but I do not get it, so I am going to give the two problems that are giving me the most trouble on my very long worksheet I have to do, maybe you guys can ...
1
vote
1answer
29 views

Integrating an equation with both cos and tan

$$\int2\cos^5x\cdot\tan^6x\cdot dx$$ $$2\int\cos^5x\cdot\frac{\sin^6x}{\cos^6x}\cdot dx$$ $$2\int \frac{\sin^6x}{\cos{x}} dx$$ $$2\int\cos^{-2}x\cdot \sin^6x\cdot \cos{x}\cdot dx$$ ...
0
votes
3answers
53 views

I have problem with Trigonometry

Tomorrow I have a test and there is one exercise in my textbook that isn't explained. Here is the exercise. ...
0
votes
1answer
31 views

Real world tangent functions

I am a high school math teacher and one of my students asked me for examples of real world tangent functions. Not using tangent to find a side length but a relationship that can be represented by a ...
0
votes
1answer
38 views

When to use what inverse trig?

When do I use $\arcsin$ and when do I need to include all of the outcomes? My gut feeling is if you have an equation like $\sin(x)=0$, then $x=0,\pi,2\pi...$ whilst if you are using it in integration ...
1
vote
1answer
40 views

When is $ 4 ab \sin^2 θ = (a+b)^2 $ ?

I know that by trial and error it is only possible when $ a=b $, but what is the actual solution process?
1
vote
0answers
25 views

Weierstrass function

I got stuck on this exercise from Prof. Tao's real analysis notes. Let $f:\mathbb{R}\rightarrow \mathbb{R}$ be the function $$f:= \sum_{n=1}^\infty 4^{-n} \sin(8^n\pi x)$$ Show that for every 8-dyadic ...