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

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2
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2answers
101 views

How to solve 4sin θ +3cos θ equals 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)
3
votes
1answer
36 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
21 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
29 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
1answer
14 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
16 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
21 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
20 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
18 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
75 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
21 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
54 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
35 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
15 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
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1answer
20 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!
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0answers
30 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
19 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
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3answers
50 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
0answers
24 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
36 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
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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
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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 ...
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vote
3answers
42 views

Problem with trigonometric equation

I am having trouble solving this equation $$4\cdot \sin \theta + 2 \cdot \sin 2\theta =5$$ Thank you for your help.
0
votes
2answers
24 views

Trig Identity Proofs

I'm having a really hard time understanding how to do these. The directions are to verify that each of the following is an identity: $$\dfrac{\csc x}{\cot x+\tan x}=\cos x$$ I have to get the left ...
0
votes
2answers
19 views

Express the following in terms of $q$.

Given that $\cos{160^{\circ}} = -q$, express $\cos70^{\circ}$ in terms of $q$. No example in the book, don't know how to do it?? I need a complete explanation.
2
votes
1answer
29 views

Can I find this trigonometric expression without a calculator?

I know that $\sin A= 0.75$ will give me the answer of $A= 48.6^\circ$ or $\ 131^\circ$. Is there a way to find what $A$ equals manually. Thank you.
0
votes
3answers
30 views

Problem with this Trigonometric Equation

I am having trouble figuring out how to solve such an equation can anyone please tell me the steps to solve it as I have been solving a lot of trigonometric equations but I am stuck in this one: ...
0
votes
1answer
24 views

Trigonometric problem

I am having trouble solving simple trigonometric equations without a calculator which I am required to be doing in my course since I cant get to understand how to get for example sin x=-1/2 I know sin ...
2
votes
1answer
38 views

Sum of fractions of squared sines

I'm trying to prove the following approximate identity for $p$ integer: $$ \sum_{l=1}^m\frac{\sin^2\left(\frac{\pi l}{p}\right)}{\sin^2\left(\frac{\pi l}{mp}\right)}\sim \frac{m^2(p-1)}{2}+O(m) $$ ...
0
votes
1answer
17 views

Simple algebraic question mixed up

I know it is very simple but do not know why I am mixed up in it $(.5)(r^2)\cfrac{20-2r}r$ how is this equal to $10r-r^2$ Sorry if it is too easy, thanks for the help.
0
votes
1answer
22 views

Trigonometric equation problem.

Simply and shortly how do I show that this $33 = 33 + 5 \cos(720\cdot t)$ is equal to this $720 \cdot t = 90.$ Thank you for your help.
2
votes
0answers
40 views

How find the range value $a^2+b^2$ if $\cos{(a\sin{x})}=\sin{(b\cos{x})}$ have no solution

if the equation $$\cos{(a\sin{x})}=\sin{(b\cos{x})}$$ have no zero solution,then $a^2+b^2$ range of value $A:[0,\dfrac{\pi}{4})$,$B: [0,\dfrac{\pi^2}{2})$,$C: ...
2
votes
4answers
22 views

Minimum value Of trigonometry expression

FIND THE MIN VALUE OF 4 cosec^2 x + 9 sin^2 x ? Please explain by both calculus and non-calculus methods ?
1
vote
2answers
15 views

Minimum value of trigonometric functions

What will be the min value of cosec x -sinx .Differentiating and setting it to zero is fetching me nothing meaningful. Plz explain how to go for such cosec and sec functions ?
0
votes
0answers
32 views

Finding the inverse of trig functions

I'm supposed to find the inverse of $$f(x) = \cos(x)+x$$ I usually just substitute $x$ for $y$ and then re-arrange. What do I do in this scenario?
2
votes
6answers
96 views

explicit expression sought

Consider the equation $$ \cos^2\phi + \alpha\sin\phi\cos\phi-\beta=0\;, $$ where $\alpha,\beta\in\mathbb{R}$. I need to find an explicit expression for $\phi$. I have tried completing the square, but ...
3
votes
1answer
38 views

Finite-case symmetry leads to infinite-case asymmetry

Formulas for sines or cosines of sums superficially appear to have a certain symmetry, specifically it looks as if sine and cosine play something like symmetrical roles: $$ \begin{align} & ...
1
vote
2answers
29 views

Complex Numbers and Hyperbolic Functions

How would you evaluate: $\mathfrak{R}\left[(1+i)\sin\left(\dfrac{(2+i)\pi}{4}\right)\right]$? I know that $\cos x = \dfrac{e^{ix}+e^{-ix}}{2}$ and $\sin x = \dfrac{e^{ix}-e^{-ix}}{2i}$. I have also ...
2
votes
1answer
34 views

Inverse trig and trigh in integration?

I have just done part (iii) of this question and can get the right answer but am a bit confused why do we take arcosh i.e. just the principle value of cosh and not the other value. I presume this is ...
0
votes
1answer
39 views

How to solve this trignometric equation?

I was given a circle with a radius of 3 and in it was a rectangle and an angle theta extending from the x axis to up with coordinates of (3 cos theta,3 sin theta) and the question asks me to show that ...
2
votes
2answers
40 views

Ordinary differential equation $y'(t)=\sin(f(t,y))$

One whose solution never makes me happy is the following: $$y'(t)=\sin(y+t)\text{.}$$ I would start by substituting $z(t)=y(t)+t$ to get an ODE in $z(t)$, but then I'm not sure about how to substitute ...
0
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1answer
41 views

How do I multiple these matrices together?

As a personal brain exercise, I've recently been trying to work out the math involved with rotating vertices around an arbitrary axis in 3D space. To do so, I've been relying very heavily on the ...
0
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1answer
16 views

Compound Angles

I'm working on compound angles formula problems, when i encountered this problem, sin(5pi/9) cos(7pi/18) I know how to use the formula, but I'm not sure how to break up these two angles into ...
0
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2answers
54 views

Is 1 rad important?

Of course radians generally come in ratios of π. So is 1 rad important/useful/special? Or, for that matter, is any integer radian measure important? Besides being approximately 57°, I can't seem to ...
2
votes
1answer
25 views

How do I simplify this difference of angles expression using conjugates?

I'm trying to fill in the gaps in my knowledge of simplifying rational expressions using conjugates, but this one stumps me. Given $\tan(\frac{\pi}{4}-\frac{\pi}{6})$, I can work the formula down to: ...
0
votes
2answers
27 views

Show this function can be defined as the limit function

Let f: $ \mathbb{R} \rightarrow \mathbb{R} $ be defined by f(x) = 1 for x $\in \mathbb{Q} $, f(x) = 0 otherwise. We can see f is not regulated. Show that f may be obtained as a limit function: f(x) = ...