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

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1answer
7 views

Find term for one angle of two in a trig function

In a right angled triangle, I know that tan(x) = 4/z and that tan(x+y) = 12/z I need to find an equation which has only tan(y). The answer is 12/z = [4/z + tan(y)]/[1-(4/z)tan(y)] but I have no ...
0
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2answers
31 views

If $\sin (B) = − \frac 1 2 $ with $B$ in third quadrant, then find $\cot (B/2)$

If $\sin (B) = − \frac 1 2 $ with $B$ in third quadrant, then find $\cot (B/2)$ I'm getting $-\sqrt{3}-2$
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0answers
14 views

Would every half angle of an angle in each quadrant be in the previous quadrant?

For example, take (5pi)/4 which is in Q3, it's half angle is (5pi)/8 which is in Q2. Is this true for every angle?
0
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1answer
13 views

If $\sin A = 4/5$ with $A$ in QII, find $\cos A/2$

For the following, assume that all the given angles are in simplest form, so that if A is in QIV you may assume that 270° < A < 360°. If $\sin A = 4/5$ with A in QII, find $\cos A/2$ I keep ...
2
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1answer
20 views

Prove this identity: $ \tan(2x)-\sec(2x) =\tan(x-\pi/4)$

I've been having a time with this problem. I tried to start with the left side but I hit a dead end quick... I then tried the right side and had a little more luck but I've hit a block. I first used ...
0
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2answers
26 views

If $\sin B = −1/2$ with $B$ in QIII, find $\cos B/2$

For the following, assume that all the given angles are in simplest form, so that if A is in QIV you may assume that 270° < A < 360°. If $\sin B = −1/2$ with B in QIII, find $\cos B/2$ Here's ...
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4answers
38 views

Prove this identity: $\sin^4x = \dfrac{1}{8}(3 - 4\cos2x + \cos4x)$.

The problem reads as follows. Prove this identity: $\sin^4x = \dfrac{1}{8}(3 - 4\cos2x + \cos4x)$. I started with the right side and used double angles identities for $\cos2x$ and a sum and then ...
1
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1answer
45 views

Prove $\cos 3\theta = 4 \cos^3\theta − 3 \cos \theta$

$\cos 3θ = 4 \cos^3 θ − 3 \cos θ$ Here's my attempt. Is it correct? Thanks! $\cos(3θ)$ $= \cos(2θ + θ)$ $= \cos(2θ)\cos(θ) - \sin(2θ)\sinθ$ $= (2\cos^2θ - 1)\cosθ - (2\sinθ\cosθ)\sinθ$ $= ...
0
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3answers
40 views

Prove this identity? $\cos t ⋅ \cos u ⋅ \cos v = \frac14(\cos(t + u + v)+ \cos(t + u - v)+cos(t-u-v))$

The problem reads as follows. Prove the identity $$\cos t⋅\cos u⋅\cos v =\frac14\big(\!\cos(t + u + v)+\cos(t + u - v)+\cos(t-u-v)\big)$$ Hint: begin with the right side and use cosine sum identity ...
1
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3answers
62 views

Range of f(x) = $\frac{\sqrt3\,\sin x}{2 + \cos x}$ [duplicate]

Can you give any idea about the range of the following function? $$f(x) = \frac{\sqrt{3}\,\sin x}{2 + \cos x}$$
2
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0answers
32 views

($\cos^4x$)($\sin^2x$) in terms of first power of cosine

I believe that I have his correct but if someone could check it and see that'd be great. Here's a pic! [IMG]http://i58.tinypic.com/2dgm5ic.jpg[/IMG]
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2answers
41 views

Show that $(1 – \cos θ – \sin θ )^2 – 2(1 – \sin θ )(1 – \cos θ ) = 0$.

Show that $(1 – \cos θ – \sin θ )^2 – 2(1 – \sin θ )(1 – \cos θ ) = 0$. What kind of formulas should I use?
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1answer
28 views

Find the value of $\theta$?

An operation maps the point $(x, y)$ on to the point $(x cos \theta, y sin \theta)$. i) Find the value of $\theta$ for which the y-axis is the image of the line $y = x$. ii) Draw a diagram to show ...
0
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1answer
30 views

Hint finding exact value of half-angle when $\tan (\theta) = {3}$

Unlike others I've tried, I'm having a hard time with this half-angle exercise: If $tan(\theta)={3}$ and $\theta$ is in QIII, find $\tan\left(\frac{\theta}{2}\right)$ Here's what I know (or think I ...
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4answers
33 views

Multiple trigonometric functions

How can you solve such a problem where multiple trigonometric functions are applied? Find the value of $\sin(\text{arc}\cot(\tan(\arccos\frac{3}{\sqrt{13}})))$.
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4answers
55 views

Is $\sin(\arcsin(x))$ equal to $x$?

I have a question. Is $\arcsin(\sin (x))$ or $\sin(\arcsin(x))$ always equal to $x$? And also for all other trigonometric ratios?
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0answers
9 views

Get Attitude from 2-axis vector

I've built a quadrotor but my 3-axis accelerometer has a fault, the Z-Axis doesn't work. I would normally get my attitude with the following code pitch = atan2(accel_X, accel_Z)*RadToDeg; roll= ...
0
votes
1answer
30 views

Writing expressions in terms of only sine

If I were to do this without these formulas, I would pull out a number that made both of the numbers(like (sqrt(3))/2 and 1/2) in the picture would be something that I could get a sine and cosine that ...
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0answers
7 views

How to properly clamp Beckmann Distribution

I am trying to implement the Cook-Torrance Microfacet BRDF shading model and I am having some trouble with the Beckmann Distribution: Beckmann Distribution with width parameter ...
0
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2answers
35 views

Was I wrong to omit angles in the solution set for this multiple angle problem?

I may have missed this in my precalculus course, but why was I wrong to omit angles that did not have a positive value for cosine? I didn't include $\frac{3\pi}{4},\frac{7\pi}{12},\frac{5\pi}{4}$ ...
1
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1answer
20 views

Check my solution to this trig inequality

Problem $1.88$ : Solve $$\cos x\lt \frac{\sqrt{3}}{2},\qquad x \in [0,2\pi]$$ I found the set of solutions to be $S=[0,2\pi]-\left[\dfrac{\pi}{6},\dfrac{11\pi}{6}\right]$ Is this correct? Thank you.
0
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1answer
23 views

Different ways to formally define trigonometric functions

When I first learnt trigonometric functions I was in highschool and obviously the explanation they gave me was mostly intuitive. Now that I have taken my first curse of calculus I learnt a formal ...
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4answers
36 views

Prove that $\sin(\frac{\pi}{3}+x)=\cos(\frac{\pi}{6}-x)$

How to prove that $\sin(\frac{\pi}{3}+x)=\cos(\frac{\pi}{6}-x)$ without using calculus just trigonometry?
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3answers
17 views

Find in terms of $p$, $\tan(-\alpha)$, $\tan(\pi - \alpha)$ and $\tan(\frac{\pi}{2}-\alpha)$.

Given that $\tan$ $\alpha = p$, where $\alpha$ is acute, find in terms of $p$, $\tan(-\alpha)$, $\tan(\pi - \alpha)$ and $\tan(\frac{\pi}{2}-\alpha)$.
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9answers
1k views

Are there 3 trig functions or are there 6 trig functions?

In my algebra class we are being taught that there are only the 3 basic trig functions (cosine, sine, and tangent). But my friend who is 2 math grade levels ahead of me is saying that there is 6 trig ...
2
votes
3answers
65 views

$\tan(x)=\cot(90^\circ-x)$??

I was looking at a mark scheme for a question I was stuck on, and I came across this. You are asked to work out the value of $\tan 75^\circ$ after you've worked out $\cos 15^\circ$ and $\sin ...
-1
votes
1answer
63 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?
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0answers
6 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 ...
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1answer
24 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.
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2answers
60 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
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1answer
16 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
103 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
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2answers
50 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
34 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
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4answers
38 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
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2answers
36 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
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0answers
16 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
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2answers
50 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
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2answers
27 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
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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. ...
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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: ...
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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
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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
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0answers
25 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
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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
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1answer
24 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
56 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. ...
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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
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3answers
37 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
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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 ...