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

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-1
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0answers
27 views

Cos(a) simplification or reduction of?

"2" to the power of "a" to the power of "cos(a)" as the index. ""cos(a)"" as the radicand. ... is it possible to rewrite with ""no"" cos(a) in the above expression...
-5
votes
0answers
48 views

Can imaginary numbers be exclude in this expression?

$$\sqrt{\cos (\alpha )} \sinh \left(\log (2) a^{\frac{1}{2} \left(e^{-i \alpha }+e^{i \alpha }\right)}\right)+\sqrt{\cos (\alpha )} \cosh \left(\log (2) a^{\frac{1}{2} \left(e^{-i \alpha }+e^{i ...
0
votes
1answer
17 views

Find all degree solutions in the interval $0^\circ \leq \theta < 360^\circ$.

Find all degree solutions in the interval $0^\circ \leq \theta < 360^\circ$. If rounding is necessary, round to the nearest tenth of a degree. $$5\sin^2 \theta − 6\cos2θ= 0$$ My work: ...
1
vote
0answers
17 views

Proving that $\sin(nx) = \sum_{j=0}^{[n/2]} (-1)^j {n \choose 2j}(\cos(x))^{n-2j}(\sin(x))^{2j}$ with induction

We have to prove: $$ \sin(nx) = \sum_{j=0}^{[n/2]} (-1)^j {n \choose 2j}(\cos(x))^{n-2j}(\sin(x))^{2j}$ with induction $$ where $[n/2]$ stand for the floor function of $n/2$. I know this formula can ...
0
votes
2answers
20 views

How do you deal with inverse trig functions that produce results outside their domain?

The problem I am facing is this: Find $\cos(X) = 4/7$ in quadrant IV (of the Cartesian plane) The next step leads me to this: $X = \cos^{-1}(4/7)$ However, I know that the domain of Cosine inverse ...
3
votes
1answer
32 views

Continued product in $\sin$ series

Find the value of the product $$(\sin 1°)(\sin 3°)(\sin 5°)\ldots(\sin 89°)$$ I tried multiplying and dividing by $2$ and then combining and then converting into cosine, but doesn't work out.
3
votes
3answers
45 views

Proving a little tough trigonometric identity

Show that $$\frac{1+\sin A}{\cos A}+\frac{\cos B}{1-\sin B}=\frac{2\sin A-2\sin B}{\sin(A-B)+\cos A-\cos B}$$ How do I get the $A-B$ term in the denominator? Is RHS to LHS easier? Thanks.
-4
votes
2answers
36 views

How do I solve this simple trigonometry question? [on hold]

I need the answer quick.I can't solve this because I have 2 variable.
0
votes
1answer
37 views

Cos(a) reduction or simplification of [on hold]

\begin{equation*} 2^{a^{\cos(a)}}\sqrt{\cos(a)}. \end{equation*} "2" to the power of "a" to the power of "cos(a)" as the index. ""cos(a)"" as the radicand. ... is it possible to rewrite with ...
0
votes
2answers
41 views

Let $\omega=\cos \theta + i \sin \theta$. Find, in terms of $\theta$, the argument of $(1-\omega ^2)^*$

Let $\omega=\cos \theta + i \sin \theta$. Find, in terms of $\theta$, the argument of $(1-\omega ^2)^*$ I started by using De Moivre's theorem and making the conjugate. Let $\alpha$ be required ...
2
votes
1answer
38 views

What is connection here between $x$ and interval: $\sin^{-1}(2x(\sqrt{1-x^2})=2\sin^{-1}x$ .

For the expression \begin{equation*} \sin^{-1}(2x(\sqrt{1-x^2})=2 \sin^{-1}x,~x\in[\frac{-1}{\sqrt2}, \frac{1}{\sqrt2}], \end{equation*} I know there is a connection between the interval and the ...
4
votes
1answer
45 views

Challenging Closed form Questions

This is a rather odd request. I was given a task to create some challenging (as much as possible) problems on Closed Form questions and also provide solutions to them. Could somebody please suggest ...
-1
votes
2answers
18 views

Integral-derivative issue

The derivative of $sin^2(x)$ is $2sin(x)cos(x)$. You can also write it as $sin(2x)$. If we integrate $\sin(2x)$ we get $-0.5\cos(2x)$ and according to calculator does not equal $\sin^2(x)$. Help? ...
1
vote
1answer
49 views

Calculating tan to power -1

I have an equation of the form $$ a = \tan^{-1}\frac{y}{x} $$ is this the same as $$ a = \frac{1}{\tan\,\left.y\middle/x\right.} $$ It has been over 20 years since doing math and I cannot find any ...
1
vote
0answers
20 views

Is it possible to derive circumference from these two points?

I have two points along one axis, call it y. I don't have the x axis coordinate because the points were taken as 1-D measurements. The angle between the points is known. Is it possible to derive a ...
3
votes
6answers
55 views

Find solutions to $\cot(x)+\csc(x)=\sqrt3$ in range $[0,2\pi]$

What is the best way to do the above? Are there any tricks I should be aware of. I know how to simplify it to $\dfrac{\cos(x)}{\sin(x)} + \dfrac{1}{\sin(x)} = \sqrt{3}$ so multiplying both sides by ...
-4
votes
1answer
19 views

question that i have [on hold]

find a value of a in [0,90] that satisfies the given statement sec a=1.529096
-2
votes
3answers
62 views

4sin²θ + 1 = 6sinθ [on hold]

Use your graphing calculator to find the solutions to the following equations for $0° ≤ \theta < 360°$ by defining the left side and right side of the equation as functions and then finding the ...
2
votes
3answers
56 views

How to integrate $\int \cos^2(3x)dx$

$$\int \cos^2(3x)dx$$ The answer according to my instructor is: $${1 + \cos(6x) \over 2} + C$$ But my book says that: $$\int \cos^2(ax)dx = {x \over 2} + {\sin(2ax) \over 4a} + C$$ I'm not really ...
0
votes
1answer
54 views

Prove the inequality, $\root3\of4\sin^2(x/2)<3(\sin x+1-x)^{2/3}$

Prove that $$\left(\sin^2{\frac{x}{2}}\right) \cdot \frac{\sqrt[3]{4}}{3} \cdot \frac{1}{{(\sin x + 1 - x})^{\frac{2}{3}}} <1$$
3
votes
2answers
48 views

Is $\sin^4 x-\cos^4 x = \cos2x$ or is it $-\cos2x=\cos2x$?

A test question I received and got wrong stated that $$\sin^4x-\cos^4x = \cos2x$$ After solving the equation from lower powers of tragicomic functions it came out ...
-2
votes
0answers
13 views

Position offsets from player's original position and angle in degrees. Trigonometry required.

Since I do not know how to explain exactly what I want too well, I'll just show you what I have that works and ask the question I have. ...
3
votes
1answer
50 views

Hard question in simple trigonometry

This question is from S.L.LONEY- If $\tan(45°+\frac{y}{2})=\tan^3(45°+\frac{x}{2})$, prove that $\frac{\sin y}{\sin x}=\frac{3+\sin^2x}{1+3\sin^2x}$. I don't know what to do. I am getting nasty ...
0
votes
1answer
31 views

How to approximate Heaviside function by polynomial

I have a Heaviside smooth function that defined as $$H_{\epsilon}=\frac {1}{2} [1+\frac {2}{\pi} \arctan(\frac {x}{\epsilon})]$$ I want to use polynominal to approximate the Heaviside function. ...
0
votes
0answers
28 views

Using axis coordination to represent rotation matrix instead of angles

Euler angles give us clear matrix for conversion of a vector from car reference $Fr^C$ to earth reference $Fr^E$. If $\vec V$ is a vector in different frames it is represented differently: $$\vec ...
1
vote
2answers
20 views

Differential Equations: Recursive Functions

Functions I have some familiarity with look so, $y^\prime(x) = \tan(x+2)$: straightforward expression of the first derivative of y as a function of x. But say I have a function, $y^\prime(x) = ...
2
votes
4answers
552 views

How can we know what cos(-75) is?

We need to prove it using the sum and difference formula. We also need to use special triangles. how? I've tried doing cos(a-b) but I did cos(-30)cos(-75)
0
votes
2answers
20 views

cos (arc csc (x+3)/4)

Write the expression as an equivalent algebraic expression involving only x. (Assume x is positive.) Here is my work: (arc csc((x+3)/4) let theta = arcsin 4/(x+3) sintheta = 4/(x+3) Then I made a ...
0
votes
2answers
17 views

If sin A = −3/5 with A in QIII, find sec (A/2)

1) 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 = −3/5 with A in QIII, find sec (A/2) Can ...
2
votes
2answers
57 views

Confusion with seeming lack of notational coherence between $\sin^{-1}(x)$ and $\sin^2(x)$

It seems that $\sin^2(x)$ is used to denote the square of whatever value $\sin(x)$ is, instead of the expected $(\sin(x))^2$. Based on that, I would assume that $\sin^{-1}(x) = \frac{1}{\sin(x)}$, ...
-2
votes
3answers
44 views

Calculate trigonometric $ \sin(2\arcsin\frac{12}{13}) $ [on hold]

I need to calculate the following trigonometric expression without a calculator: $ \sin(2\arcsin\frac{12}{13}) $
4
votes
5answers
44 views

Factorising trigonometric functions

In order to factorise $x^2-1$ one way of thinking about it would be to set it equal to zero and solve to get $x=1$ and $x=-1$. You can then write $x^2-1=(x+1)(x-1)$ Can we do the same with ...
2
votes
3answers
68 views

What are “tan” and “atan”?

As the title says, I'm confused on what tan and atan are. I'm writing a program in Java and I came across these two mathematical functions. I know tan stands for tangent but if possible could someone ...
0
votes
1answer
16 views

Probability function of Acos(x)

Let's say I have a signal $y(t) = Acos(2\pi f_c t)$, where $f_c$ is the carrier frequency and $t$ is the independent variable. Since I work with discrete signals i sample this signal with a sampling ...
1
vote
1answer
20 views

Finding the volume of the following solid using triple integrals

Find the volume of the solid in the first octant bounded by the coordinate planes, the cylinder $x^2 +y^2 =4$ and the plane $z+y=3$. I found the integral bounds just fine. So I have $\int_{0}^{2} ...
0
votes
3answers
62 views

How to solve $x=\arctan(\tan(-8))$?

How to solve $x=\arctan(\tan(-8))$? My instinct would just be to say $x=-8$ but I think that there is some restrictions with domains of $\tan(x)$ any help?
1
vote
2answers
53 views

integrating sine raised to fraction

Not super math-y myself, but writing a small script for an algorithm where sine is raised to the power of a fraction. Found lots of examples for sine raised to 1, 2, 3, and ways to solve for this, but ...
0
votes
1answer
38 views

Constructibility of $\arctan\left(\frac{1}{2}\right)$

I would like to show that $\arctan\left(\frac{1}{2}\right)$ is not a constructible number. I would like to use the following lemma: Let $P(x)=x^3+ax^2+bx+c$ a polynomial with ...
2
votes
2answers
35 views

what is the lowest point of a tilted elliptical plate?

I'd like to know the lowest point $z_\min$ of an ellipse with radius $r_x, r_y$ in (Euclidian) XY that's tilted in XYZ - first rotated around X axis by $\gamma$, then rotated around Y axis by ...
1
vote
3answers
35 views

Help solve for length $PQ$

how do I approach this question using simultaneous equations with trig and or pythag??? Solve for length $PQ$ Cheers bob
0
votes
0answers
22 views

How to approximate a trigonometric to make less computation complexity

I having a trigonometric function such as $$ p_2(s) = \begin{cases} \frac {1}{(2 \pi)^2}(1-\cos (2 \pi s)), & \text{if $s \le1$ } \\ \frac {1}{2 }(s-1)^2, & \text{if $s >1$ } ...
0
votes
7answers
105 views

Evaluate the limit $\lim\limits_{ x \to 0} \frac {\sin 5 x } {\sin 2 x }$

$$\quad\quad \lim_{ x \to 0} \frac {\sin 5 x } {\sin 2 x } $$ I don't know how to start, should I multiply by something... to simplify the expression or ...?
2
votes
3answers
26 views

Investigating the bijectivity of $ 2 x + |\cos(x)| $.

The question asks if the function $$ f(x) = 2 x + |\cos(x)| $$ if (one-one, onto), (many-one, onto) or (one-one, into). After a long process of plotting the graph, I managed to guess it’s one-one and ...
0
votes
0answers
14 views

Sine and cosine graph transformation

I'm having some difficulties with this question A bike is on a stand such that the highest point of the back wheel is 47 inches above the ground. If the pedal is turned counter clockwise, the back ...
1
vote
4answers
22 views

Finding the exact values of trig functions in a quadrant

I need some help solving some questions because I have no idea how to solve them, and some explanation would be appreciated. The questions says: Given $\cot\alpha=\frac{\sqrt{13}}{6}$ and $\alpha$ ...
-1
votes
1answer
37 views

Triangles and law of sine, cosine question [on hold]

Im having problems with this question and I've tried lots of approaches yet keep getting the similar or a close answer to what im getting an its always wrong
3
votes
0answers
33 views

Triangles, sine and cosine problem

Hi everyone I tried solving this countless times but I always get the wrong answer! what I did first is 600/tan(46) - 600/tan(40) and that sounded reasonable to find the answer! but I keep getting it ...
0
votes
2answers
51 views

Rearranging a system of trigonometric equations [on hold]

I have the following two equations: $$\begin{align}17\,t\cos\theta &= x + 8\,t\sin\alpha \\ 17\,t\sin\theta &= y + 8\,t\sin\alpha.\end{align}$$ where $x$, $y$ and $\alpha$ are known values, ...
4
votes
1answer
44 views

Using trigonometry to predict future position

Intro I'm currently creating an AI for a robot whose aim is to shoot another robot. All I want to do is to be able to calculate at what angle to shoot my bullet, so that it hits my enemy, with the ...
1
vote
1answer
29 views

3D Trigonometry Problems [on hold]

I need help with solving this problem. I just don't know how to approach it. If I had another side, I could solve it using Sine Law, otherwise, I'm not sure... It's number 49 I need help with. ...