2
votes
2answers
33 views

How to find the period of the sum of two trigonometric functions

I want to know if there exists a general method to find the period of the sum of two periodic trigonometric function. Example: $$f(x)=\cos(x/3)+\cos(x/4).$$
3
votes
1answer
37 views

Range of $f(x)=\frac{\sin x -1}{\sqrt{3-2\cos x-2\sin x}}$ for a specified domain

We are asked to find the range of the function $$f(x)=\frac{\sin x -1}{\sqrt{3-2\cos x-2\sin x}}, \;\;\text{for}\;0\le x\le2\pi$$ I tried to find the range of each basic function of cos and sin then ...
0
votes
4answers
66 views

Derivative with respect of a function

i have a function of two variables: $f(\theta,\phi) = \theta \sin(\phi)$ and i have to differentiate $f(\theta,\phi)$ with respect to: $1 - 0.5\theta^2$ That is: ...
1
vote
1answer
33 views

Evaluate position of first secondary maximum of $\frac{\sin N (x/2)}{\sin (x/2)}$

The function $$f(x) = \displaystyle \left | \frac{\sin \left( N \displaystyle \frac{x}{2} \right)}{\sin \left( \displaystyle \frac{x}{2} \right)} \right |$$ when evaluated for $x > 0$, has its ...
1
vote
1answer
28 views

Laplace Transform with sin and cos

Hi I am having trouble figuring out the solution of this Laplace transform: $$L_t{(u(t- \pi)(2\cos(t)-3\sin(3t))}$$ Where I am stuck if I am even on the right track is: $$L_t{(u(t- ...
1
vote
5answers
53 views

Finding the range and domain of $f(x)=\tan (x)$

I am attempting to find the range and domain of $f(x)=\tan(x)$ and show why this is the case. I can seem to find the domain relatively well, however I run into problems with the range. Here's what I ...
0
votes
1answer
34 views

Finding the range and domain of $h(x) = \sec (x)$

I am attempting to show how to find the range and domain of $h(x) = \sec (x)$. Here's my working so far. Consider $h(x) = \sec (x)$, which is defined as $h(x) = \sec (x)=\frac{1}{\cos(x)}$. We know ...
1
vote
1answer
57 views

finding exact value of $\sec^{-1} 5$

Find the exact value of $\sec^{-1} 5$ (decimal answer). I know that $\sec^{-1}5=\cos^{-1}\dfrac{1}{5}$, but I don't know how to proceed from here. I drew a right triangle with sides $1$ and $5$ ...
0
votes
2answers
45 views

Period of $\frac{\sin(Ny)}{sin y}$ with $N$ odd?

The function $$f(y) = \displaystyle \frac{\sin(Ny)}{\sin y}$$ is periodic with period $2 \pi$ in general. But tracing the graphic of that function for $N$ odd it seems that for $0 \leq x < \pi$ ...
1
vote
1answer
42 views

Handy way to find the $x$ value where $\sin x \cos \left( \frac{\pi}{2} \sin x \right)$ is maximum?

Like in the title, is there a handy way to compute the $x$ values for which the function $$f(x) = \sin x \cos \left( \frac{\pi}{2} \sin x \right)$$ reaches its maxima? The derivative is $$f'(x) = ...
0
votes
1answer
8 views

Sinus curve with elbows / round steps?

Can I calculate a sinus function that has kind of elbows / round steps in it ? Or if I could get hold on the second curve. I need one of these functions for some graphical design. How would the ...
0
votes
1answer
20 views

Inverting complicated function (possibly using secant root finder)

So I have the following equation from the 2002 paper "A Rapid Hierarchical Rendering Technique for Translucent Materials" http://graphics.ucsd.edu/~henrik/papers/fast_bssrdf/fast_bssrdf.pdf Here is ...
0
votes
3answers
60 views

Find how far runners travel on a circular track (trig)

-How far has each runner traveled after 8 seconds? Though I just had to convert the rad/sec to rev/sec to get yards then multiply that by 8 seconds, but that isnt correct. Find the angle θ, in ...
0
votes
3answers
61 views

How to make a cos function into a sin function

I need to convert this equation into a sin function: f(x) = 12 cos(2x + 1) − 3 I know cos(x)= sin (pi/2 -x) but other than that I dont know how to solve this problem
3
votes
6answers
154 views

How do I verify that $\sin (\theta)$ and $\cos (\theta)$ are functions?

I am studying pre-calculus mathematics at the moment, and I need help in verifying if $\sin (\theta)$ and $\cos (\theta)$ are functions? I want to demonstrate that for any angle $\theta$ that there ...
0
votes
1answer
33 views

how to solve this equation $z=yb\cot(bx/2)$?

how to solve this equation $z=yb\cot(bx/2)$? $b$ is unknown, the $x,y,z$ are known numbers, and $x\ne0,b>0$, we want to have the solution for $b$. Until now I have no idea about this.
5
votes
3answers
72 views

How to calculate the range of $x\sin\frac{1}{x}$?

I want to find the range of $f(x)=x\sin\frac{1}{x}$. It is clearly that its upper boundary is $$\lim_{x\to\infty}x\sin\frac{1}{x}=1$$ but what is its lower boundary? I used software to obtain the ...
2
votes
3answers
68 views

How do I evaluate integrals that involve the signum ($\text{sgn}$) function?

For example, I want to evaluate $$ \displaystyle \int_{0}^{2\pi} \left| \sin x \right| \text{ d}x $$ and I already know that: $$ \displaystyle \begin{aligned} \int \left| \sin x \right| \text{ d}x ...
0
votes
2answers
47 views

$\cos(x)$ domain and range

I'd like to refer the following answer: http://math.stackexchange.com/a/628992/130682 @robjohn claims that: ...
2
votes
1answer
55 views

Do you use degrees or radians for trig functions?

I was just wondering if you use degrees or radians in trig functions. For example if I have a degree of 0.5 would I do: Sin(0.5) or would I have to convert that to radians? Or does it not matter ...
-2
votes
1answer
52 views

Why do sine and cosine functions intersect the multiples of pi at x-axis?

Why do sine and cosine functions intersect the multiples of pi at x-axis? Maybe a dumb question, but I can't figure out why is that... And since $\pi$ is a transcendental number, we can't find the ...
0
votes
2answers
61 views

Is this true about the inverse sine?

It is known that $ \sin(-x)=-\sin x \ $. Bbut when we say: $$ \arcsin(-x)=-\arcsin x$$ Is this true? Is it the same with the other trigonometric functions "inverse"?
3
votes
1answer
54 views

Finding the equation for a sinusoidal cycle/function given points.

We are given the population of a fictional animal at different years: $$\begin{array}{l|r} \textrm{Year} & \textrm{Population}\\\hline 1945 & 347,0000\\ 1955 & 76,000\\ 1965 & ...
2
votes
3answers
45 views

On what interval does the function $f(x)=-\sin x$ increases and …

Can you explain me how do I find the intervals where the function:$$f(x)=-\sin x$$ is increasing and decreasing. Thank you!
1
vote
2answers
77 views

How to find $\frac{d^{40}y}{dx^{40}}$, when $y= \sin x$? [closed]

What approach would be ideal in finding $\frac{d^{40}y}{dx^{40}}$, when $y= \sin x$?
2
votes
2answers
45 views

Is $\sec^{-1}(\sec(\pi/2)) = \pi/2$?

I think it shouldn't be defined as $\pi/2$ is not in the range of the function $\sec^{-1}(x)$ Wolfram confused me by giving the answer as $\pi/2$ : Link But it mentions on another page that $\pi/2$ ...
1
vote
0answers
35 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 ...
5
votes
2answers
110 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
3answers
97 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? $$f(x) = \frac{\sqrt{3}\,\sin x}{2 + \cos x}$$
0
votes
4answers
68 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
17 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 ...
1
vote
1answer
27 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.
1
vote
2answers
44 views

Sin & Cos Equation/Relation

If sin(x) = 0.3, find cos(pi-x) how i would solve this: let x = sin-1(0.3) solve for cos(pi-[sin-1(0.3)]) Is there a way to solve this by hand? Is the above method wrong?
1
vote
2answers
74 views

Find the range of a function

How to find the range of the following trigonometric function $\sin^2x-5\sin x-6$. Can some one help me out. Thank you
-2
votes
3answers
142 views

Limit of infinite loops of sin x as n tends to infinity [duplicate]

Show that $$lim_{n\to\infty} \text {sin sin ... sin x} = 0 $$ for all x. Note that the n here refers to the number of sin in the expression above.
3
votes
2answers
67 views

Domain and range of a function.

Find the domain and range of the function $$f(x)=\frac{1}{\sqrt{[\cos x]-[\sin x]}}$$ Where [] denotes the greatest integer function. I started as $[\cos x]-[\sin x]\gt0$ $\implies \cos ...
0
votes
1answer
35 views

Trigonometric functions over arbitrary angles

Trigonometric functions over obtuse or arbitrary angles doesn't make sense. We can only imagine for eg. sin(x) for angles < 90 degrees because it represents the ratio of the opposite and ...
1
vote
1answer
15 views

Arc Tangents and Equation

For one of the problems in my book, it requires you to put the arc tangent into the 2piK equation and solve for the arc tangents and lie in [0,2pi]. For: arctan(117)+piK the answers are 1.5622 and ...
1
vote
1answer
79 views

Inverse Trig Functions with Double Angle Formulas

I am studying for a quiz tomorrow and one of the sections I am studying involves rewriting quantities as algebraic expressions of $x$. One of the problems I am having trouble with is: $$\sin ...
1
vote
2answers
50 views

Inverse Trigonometric Functions problem

Hello mathematicians Today I am stuck with a rather simple problems. $$y_1=\sin(\frac{1}{2} \arccos(\frac{4}{5}))$$ $$y_2=\cos(\frac{1}{2}\arccos(x))$$ I am required to simplify both of the above ...
4
votes
1answer
100 views

I need to understand $t=\cos(x) \implies x=\arccos(t)$

I need to understand this because I think that I don't know the meaning of arc... $t=\cos(x) \Rightarrow x=\arccos(t)$ ?? Thanks
0
votes
0answers
32 views

Inverse ease-in-out parametric function

I'm trying to create an inverse ease-in-out function that given values from 0 to 1, produces values from 0 to 1. Opposite of a typical ease-in-out function, though, I want it to start accelerated, ...
2
votes
2answers
43 views

How to calculate the undefined limit of this trig function?

I have to simplify this function : $$ f(x) = (x-2)\tan\left(\frac {\pi}{x}\right)$$ In order to calculate $\lim\limits_{x\to2}f(x)$ since $\lim\limits_{x\to2}(x-2) = 0$ and ...
2
votes
4answers
86 views

How to solve this limit of a function? ($\cos^3x$)

So I'm having trouble with the following limit: $$\lim_{x\to0}{\frac{1-\cos^3x}{x\,\sin x}}$$ Sorry to bother again, but I was never good at solving limits. Really, I don't know what to do with ...
0
votes
3answers
54 views

How to solve this limit of a function?

So I'm having trouble with the following limit: $$\lim_{x\to0}{\frac{x\sin x}{1-\cos2x}}$$ Tried to solve it multiple times and failed, so i posted it here... If possible, solve it in steps, so I ...
1
vote
2answers
304 views

Proof for the formula of sum of arcsine functions $ \arcsin x + \arcsin y $

It is known that the following holds good: $$ \arcsin x + \arcsin y \\ \begin{align} &=\arcsin( x\sqrt{1-y^2} + y\sqrt{1-x^2}) \;\;;x^2+y^2 \le 1 \;\text{ or }\; x^2+y^2 > 1, xy< 0\\ ...
-2
votes
3answers
75 views

Find the general solution of $\sin(4t) + \sqrt3 \cos(4t)$

How to find the general solution of the equation $\sin 4t + \sqrt{3} \cos 4t$ in exact form. so what I know is $\sin 4t + \sqrt3 \cos 4t = 2 \cos(4t - \frac{\pi}{3})$ The answer is $t = ...
1
vote
1answer
41 views

Can't understand logic behind review answer.

Sorry about the title, wasn't sure how to make it more descriptive of my question. I'm doing unit review right now, and looked at the online posted review answers by our teacher. I understand the math ...
0
votes
2answers
51 views

Is $\sqrt{x}(\sin{1\over x}+x)$ uniformly continuous on $(0,\infty)$?

Is $\sqrt{x}(\sin{\dfrac{1}{x}}+x)$ uniformly continuous on $(0,\infty)$? At first, I tried to take the derivative and show it is bounded, but derivative is a bit complicated, so I'm suspecting ...
1
vote
1answer
89 views

Graphs that Behave Strangely

What exactly are $y =\cos(xy)$ or $y = x^y$? I tried graphing them on OS X grapher and the first gave me this ridiculous looking graph, with sharp angles and lines everywhere, it seemed like it was ...