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

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5
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3answers
48 views

Why is $\int^{\infty}_{0}{(1-\cos x)\over{x^{2}}}dx = \frac\pi{2}$

I have been having trouble understanding Fourier series and analysis in one of my classes. This is one problem from the text and we have to show that this is true. I have done other problems related ...
0
votes
1answer
20 views

Polar graph question

Can you only graph periodic functions using polar graphing? I'm not really understanding this I guess. It you are to get all of the x and y values on a finite graph, then the original must be ...
5
votes
1answer
57 views

Are there any constants other than $\pi$ that give rational or known irrational values for $\cos(\theta)$?

For example: $\cos(\frac{\pi}{3}) = \frac{1}{2}$ $\cos(\frac{\pi}{4}) = \frac{\sqrt{2}}{2}$ Is there any other constant $\theta$ such that $\cos(k\theta)$ is rational or a known irrational where ...
2
votes
1answer
36 views

Explain how the following is equal to $2\cos x$.

The question was Prove $$\frac{1+\sin2x+\cos2x}{\cos x+\sin x}=2\cos x$$ I simplified it using several trigonometric identities, what I got is this "$\dfrac{2\cos^2 x + 2\cos x \sin x}{\cos x + ...
0
votes
2answers
29 views

Trigonometry prove

here the question is that i can prove that the left side=the right side if i use the variable x but if we take (2x=pi on the left side) and (x=pi/2 on the other side) then the equation is not ...
1
vote
2answers
50 views

Is $\sqrt{1-\sin ^2 100^\circ}\cdot \sec 100^\circ = 1$ or $-1$?

The equation will simplify to \begin{align} & = \sqrt{\cos^2 100^\circ}\cdot \sec100^\circ \\[8pt] & = \cos100^\circ\cdot\sec100^\circ \\[8pt] & = 1 \end{align} But the answer key says ...
2
votes
3answers
30 views

Finding tan(A+B)

So I know that $$ \tan(A+B) = \frac{\tan(A) + \tan(B)}{1 - \tan(A) \tan(B)}, $$ but I don`t know how to find $\tan(B)$ for the following problem: If $\tan A = 2/3$ and $\sin B = 5/\sqrt{41}$ and ...
1
vote
3answers
44 views

Area of a Parallelogram

The sides of a parallelogram measure $10$ cm and $18$ cm. One angle of the parallelogram measures $46$ degrees. What is the area of the parallelogram, to the nearest square centimeter? I'm ...
1
vote
1answer
62 views

Expansion of $\sin(a_{1}+a_{2}+…+a_{n})$?

We know this formula: $$\sin(a+b)=\sin a\cdot\cos b+\sin b\cdot\cos a$$ So how to find the of the expansion of this $$\sin(a_{1}+a_{2}+\cdots+a_{n})=\,?$$
1
vote
0answers
17 views

How to approach sketching sine and cosine graphs with transformations

Any tips or suggestions in sketching these graphs quickly, and in ONE go? In exams, I don't want to spend ages re-drawing the original sine/cosine graph, one by one, following each new ...
2
votes
6answers
44 views

General solution for squared trigonometry questions: $\cos^2 x = 1$

$\cos^2 x = 1$ How do you solve trig equations with a power? Unsure what to do with the square? I get this $\frac{1+\cos2x}2 =1$ $\cos2x =1$ $2x=2n\pi\pm0$ $x=n\pi$ but the answer says $\pm ...
1
vote
2answers
25 views

Need help Proving Identities

Prove the Identity: $$\frac{1 + \cos \theta}{\sin \theta} + \frac{\sin \theta}{\cos \theta} = \frac{\cos \theta + 1}{\sin \theta \cos \theta}. $$
1
vote
2answers
27 views

Looking at an angle rotated

Suppose you have an angle of degree theta painted on the ground at a spot. You are standing d distance away and looking at it from a height of h and from your perspective the angle appears to be of ...
0
votes
1answer
38 views

A Question Regarding Trigonometry

For question 7, I have figured out the angles for 2 triangles, the one with RJh and the one with PJh. I don't know what to do after that.
1
vote
3answers
27 views

Find the value of $\sin(B-A)$.

If $A$ is an acute angle whose tangent is $\frac{15}{8}$ and $B$ is and obtuse angle whose sine is $\frac{12}{13}$, find $\sin (B-A)$. [Without calculators] I suppose I gotta use this formula: $\sin ...
0
votes
1answer
43 views

No. of real solutions of the equation $2 \cos (\frac{x^2 + x}{6}) = 2^x + 2^{-x} $

How many real solutions are there of the equation $2 \cos (\frac{x^2 + x}{6}) = 2^x + 2^{-x} $? Please illustrate.
2
votes
2answers
32 views

If $\sin A = \cfrac{3}{5}$ with $A$ in QII, find $\sec2A$.

If $\sin A = \cfrac{3}{5}$ with $A$ in QII, find $\sec2A$. I'm getting $\sec2A=\cfrac{25}{7}$. Is that correct?
4
votes
6answers
109 views

Exact value for $\cos 36°$

Good morning! I'm having trouble with this problem... It's just taking me forever and I'm worn out and I'm lost on how to use a double angle identity for $72=2⋅36$ The problem reads as follows An ...
0
votes
0answers
17 views

What is the Winding Function? [on hold]

I've often heard of a mnemonic device called "SOH-CAH-TOA" used to learn about sine, cosine and tangent. But many of my math peers tell me that this device is not very good because it doesn't give an ...
0
votes
0answers
18 views

combine $\cos2t+\sqrt{\sin2t}$ a single wave of form $A \cos (wt-\theta)$

Combine $\cos2t+\sqrt{\sin(2t)}$ in a single wave of form $$A \cos {(wt-\theta)}$$ Hence plot arough sketch of the graph of the wave
5
votes
2answers
86 views

Solving complex trig functions: $\sin2x + \sin3x = \frac{\sqrt{3}}2$

How to solve: $$\sin(2x) + \sin(3x) = \frac{\sqrt{3}}{2}$$ where $x$ is in $[-\pi,\pi]$? I have no idea what to do with the $\sin(2x) + \sin(3x)$. Am I supposed to factorise, differentiate, is ...
1
vote
1answer
31 views

sum of an arctan series using mathematical induction

How to solve this problem using mathematical induction: $$\arctan (1) + \arctan \Big(\frac13\Big) + ... + \arctan \bigg(\frac{1}{n^2+n+1}\bigg)=\arctan (n+1)$$
0
votes
1answer
16 views

Find term for one angle of two in a trig function

In a right angled triangle, I know that $\tan (x) = \cfrac{4}{z}$ and that $\tan(x+y) = \cfrac{12}{z}$. I need to find an equation which has only $\tan(y)$. The answer is $\cfrac{12}{z} = ...
0
votes
1answer
34 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 $-\sqrt{3}-2$
1
vote
1answer
22 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
votes
1answer
17 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
votes
1answer
28 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
votes
2answers
30 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 ...
2
votes
6answers
63 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
vote
1answer
50 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
votes
3answers
45 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
vote
3answers
66 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
votes
0answers
39 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]
0
votes
2answers
46 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?
-1
votes
1answer
30 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
votes
1answer
52 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 ...
0
votes
4answers
33 views

Multiple trigonometric functions

How can you solve such a problem where multiple trigonometric functions are applied? Find the value of $\sin(\text{arc}\cot(\tan(\arccos\frac{3}{\sqrt{13}})))$.
0
votes
4answers
58 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?
0
votes
0answers
10 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 ...
0
votes
0answers
10 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
votes
2answers
36 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
vote
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
votes
1answer
24 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 ...
0
votes
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?
0
votes
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 $\tan(\frac{\pi}{2}-\alpha)$.
14
votes
9answers
2k 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
69 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
64 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
1answer
11 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 ...