2
votes
3answers
33 views

Proving that $\dfrac{\tan(x+y)-\tan x}{1+\tan(x+y)\tan x}=\tan y$

Edit: got it, silly mistakes :) I need to prove that $\dfrac{\tan(x+y)-\tan x}{1+\tan(x+y)\tan x}=\tan y$ $$=\frac{\tan x+\tan y-\tan x+\tan^2x\tan y}{1-\tan x\tan y+\tan^2x+\tan x\tan y}$$ ...
1
vote
1answer
44 views

Trying to find an $\arctan(x/y)$ identity.

I have this equation : $$\theta = \arctan\left(\tfrac xd\right) + \arctan\left(\tfrac yd\right).$$ $\theta$ is an angle and I am trying to express $d$ as a function of $\theta$. So is there a way ...
0
votes
1answer
17 views

Finding the vertical shift of a sinusoidal function

I'm currently studying sinusoids, I've been given a graph with a few key points and have been told to find a cosine function which fits it. When it comes to finding the vertical shift of the graph the ...
1
vote
2answers
41 views

$m\cos^2{\theta} + n\sin^2{\theta} < l \implies \sqrt{m}\cos^2{\theta} + \sqrt{n}\sin^2{\theta} < \sqrt{l} $

Prove that $m\cos^2{\theta} + n\sin^2{\theta} < l \implies \sqrt{m}\cos^2{\theta} + \sqrt{n}\sin^2{\theta} < \sqrt{l} $ for every $m, n, l >0$.
1
vote
1answer
109 views

What is the value of $\csc^2\frac{\pi}{14}+\csc^2\frac{3\pi}{14}+\csc^2\frac{5\pi}{14}$? [duplicate]

How to compute $$S=\csc^2\frac{\pi}{14}+\csc^2\frac{3\pi}{14}+\csc^2\frac{5\pi}{14}$$ I tried to rewrite it in terms of $\sin$ $$ ...
-1
votes
0answers
29 views

trigonometric equation (proof answer) [on hold]

hi,all as you can see in the picture there are two parts that need to be proof. first is based on (b) and second based on (a) for the first equation, i already got the answer which is d3=2dm2. ...
2
votes
1answer
73 views

If $\sin \phi$ and $\tan \phi$ are the roots of the equation $ax^2+bx+c=0$, compute $b^2-c^2$

If $\sin \phi$ and $\tan \phi$ are the roots of the equation $ax^2+bx+c=0$. Then $(b^2-c^2) = $ $\bf{Options::}$ $(a)\;\; 4ac\;\;\;\;\;\;(b)\;\; a^2\;\;\;\;\;\;(c)\;\; 4bc\;\;\;\;\;\;(d)\;\; ...
1
vote
2answers
92 views

What is $\frac{2x}{1-x^2}$ when $x=\sqrt{\frac{1-\cos\theta}{1+\cos\theta}}$?

If $$x=\sqrt{\frac{1-\cos\theta}{1+\cos\theta}}$$ Find $$\frac{2x}{1-x^2}$$ I got till here by simplification by taking the previous value of x, ie, ...
-1
votes
1answer
47 views

how to prove that $\cos n\pi=(-1)^n$?

I'm asked to prove that $$\cos n\pi=(-1)^n\qquad n\in\mathbb {Z}$$ I'm not sure how to approach the problem, I want to know if there is a different way to use induction
1
vote
3answers
15 views

A right triangle has one leg twice as long as the other. Find a function that models its perimeter P in terms of the length x of the shorter leg.

A right triangle has one leg twice as long as the other. Find a function that models its perimeter P in terms of the length x of the shorter leg. I have tried adding 2x + x for the two legs, however ...
1
vote
2answers
18 views

Trigonometric equation $\tan(\frac{\sqrt{3}x}{2})=-\sqrt{3}$

I want to solve a trigonometric equation below: $$\tan(\frac{\sqrt{3}x}{2})=-\sqrt{3}$$ What is the value of $x$ for $x>0$ Thank you for your help.
0
votes
1answer
14 views

How do I find and list compositions for (f) and (g)?

Ok, I've literally just spent the last 2 hours just to figure out two compositions problems for homework, and I've about had it. Anyone here that can help? Problem 1 $$ f(x) = 2x(2) - x -3 $$ $$ ...
-1
votes
1answer
25 views

How to convert parametric equation of a curve to Cartesian equation? [closed]

Eliminate the parameter to find a Cartesian Equation of the curve represented by $x=\tan^2t$, $y=\sec t$.
4
votes
3answers
209 views

Find all values for cos(i)

In my Differential Equations class recently we have learned about Euler's Formula and Fourier Series. I am given the problem ...
8
votes
5answers
117 views

Prove $3(\sin x-\cos x)^4 + 6(\sin x+ \cos x)^2 + 4(\sin^6 x + \cos^6 x) -13 = 0$

Q) Prove that $3(\sin \theta-\cos \theta)^4 + 6(\sin \theta+ \cos \theta)^2 + 4(\sin^6 \theta + \cos^6 \theta) -13 = 0$ Source: Trigonometric Functions, Page 5.9, Mathematics XI - R.D. Sharma ...
1
vote
1answer
35 views

How many points to span a goniometric wave and how to construct the goniometric function

I have two questions concerning the spanning of a simple trigonometric function: What is the minimum number of points to define/span a "simple" trigonometric wave in two dimensions? Is it possible ...
0
votes
2answers
21 views

Find angle $\alpha$ from a complex vector

I'm trying to solve this problem from a Russian book: Find the angle which is needed to rotate the vector $3\sqrt{2} + i2\sqrt{2}$ to obtain the vector $-5+i$. EDIT: $\tan\dfrac{\pi}{6} \neq ...
2
votes
2answers
50 views

Calculate $n$ points having equal cartesian distance over a single sine wave

I'd like some help figuring out how to calculate $n$ points of the form $(x,\sin(x))$ for $x\in[0,2\pi)$, such that the Cartesian distance between them (the distance between each pair of points if you ...
0
votes
1answer
18 views

If $\tan^2\theta=1-e^2$, then the value of $\sec\theta+\tan^3\theta \csc \theta$ is

If $\tan^2\theta = 1-e^2$,then the value of $\sec\theta$ + $\tan^3\theta \cdot \csc\theta$ is... NOTE: $1/\cos\theta +\cos^3\theta/\sin^3\theta \cdot 1/\sin\theta$ multiply: $\sin^2 ...
0
votes
4answers
48 views

Physics problem, stuck in algebra.

I end up with the equations; $$u=u_1' \cos(a)+u_2' \cos(b)$$ $$u_1' \sin(a)=u_2' \sin(b)$$ $$u^2=u_1'^2+u_2'^2$$ I have to show that $$a+b=\frac{\pi}{2}$$ $x'$ isn't the derivative of $x$, it's a ...
1
vote
1answer
35 views

Trigonometric inequality question [closed]

Let $0 < A < \frac {\pi}{2}$ and $0 < B < \frac {\pi}{2}$. (a) prove that $\sec^2 A + \csc^2 A \cdot \csc^2 B \cdot \sec^2 B \geq 9.$ (b) determine values of $\sec A$ and $\sec B$ when ...
1
vote
2answers
43 views

Expressing $ 12\sin( \omega t - 10) $ in cosine form

$$ 12\sin( \omega t - 10) $$ I understand how it's solved when using the graphical method, however I'm having trouble understanding something about the trigonometric identities method. The solution ...
1
vote
2answers
27 views

Rearranging equation $t = \frac{T}{2\pi} (\psi - \epsilon \sin \psi)$ in terms of $\psi$

I was playing around with the maths for orbits and trying to make a parametric equation that, well.. worked. I found a worksheet with parametrics with another variable ($\psi$), but I wanted to be ...
7
votes
2answers
110 views

Is $f(x)=10$ a periodic function?

I am not getting satisficatory explanation for this. Clearly $f(x+T) = f(x)$ for all values of $T$. If we assume it is periodic, does this mean period = $0$?
0
votes
2answers
39 views

What is the y-cooridinate for the point on the curve with x-cooridante 20?

What is the y-coordinate for the point on the curve with x-coordinate 20? $F. 160$ $G. 162$ $H. 164$ $J. 166$ $K. 168$ The explanation says "The correct answer is G. If the x-coordinate is 20, ...
0
votes
1answer
44 views

What trig. identity would help solve $2 + \cos(2x) = 3\cos(x)$?

I need help with a homework question that has me puzzled. I need to solve the following equation: $$2 + \cos(2x) = 3\cos(x)$$ I don't see a good trig identity to apply. I tried $\cos(2x) = ...
3
votes
3answers
102 views

Problems with trigonometry getting the power of this complex expression

I'm here because I can't finish this problem, that comes from a Russian book: Calculate $z^{40}$ where $z = \dfrac{1+i\sqrt{3}}{1-i}$ Here $i=\sqrt{-1}$. All I know right now is I need to use ...
1
vote
4answers
41 views

Calculating the angle for a path between two nodes in a graph

I want to (programatically) draw an edge between two nodes in a graph, starting on the outside of the nodes. Below is an illustration of what I'm (poorly) trying to describe: I have the $(x,y)$ ...
2
votes
3answers
38 views

$x$-intercept of cosine graph

I am having problems understanding how to find the $x$-intercept of a cosine graph. Example: $10\cos(x/2)$ Answer:$((2n + 1)\pi , 0 )$ I have the answer just need help understanding the steps, ...
0
votes
1answer
41 views

How to find limits involving trigonometric functions as $x\to 0$?

Problem: find the limit as $x\rightarrow 0$ of $\dfrac{\tan(3x)}{\sin(2x)}$ $\dfrac{(\sin(2x) + 3)}{(\cos(7x)-8)}$ Note I am able to solve the first one using l'Hopitals, but I really want to be ...
0
votes
1answer
44 views

Find distance, given angles of elevation

Write an equation giving the distance d between the plane and observation post in terms of $\theta$ and $\phi$. Is this correct? when using the Law of Sines answer: $a/\sin\theta = c/\sin C$ ...
0
votes
3answers
74 views

How do I solve the trigonometric equation $\sec^3x - 2 \tan^2 x = 2$? [closed]

A friend asked to me how could she resolve this equation, but I don't know how to resolve it?? Could you help me?. The equation is : $\sec^3x - 2 \tan^2 x = 2$ Note: She told me that I can use ...
1
vote
1answer
79 views

What is the distance from the boat to the shoreline? [closed]

A boat is sailing due east parallel to the shoreline at a speed of 10 miles per hour. At a given time, the bearing to the lighthouse is S 70° E, and 15 minutes later the bearing is S 63° E (see ...
0
votes
4answers
168 views

Manipulating a trigonometric equation involving $\tan^2(3\theta)$ [closed]

If $\tan^23\theta = 1$, how do I manipulate the equation so I can make $\tan\theta$ the subject? I forgot how to do these since it has been a long time. I tried searching before posting. My answer is ...
1
vote
3answers
52 views

Bearings question

Kim leaves his house and walks for $2$ km on a bearing of $155^\circ$. How far south is Kim from his house now, to $1$ decimal place? I don't know where to start at all, the correct answer is ...
2
votes
1answer
36 views

Trigonometric Identity problem involving cot

Simplify $\displaystyle\frac{\cot25 + \tan65}{\cot25}$ My attempt is: $$\frac{\cot25 + \tan65}{\cot25}=\frac{\cot25 + \cot(90 - 65)}{\cot25}=\frac{\cot25 + \cot25}{\cot25}= \frac{\cot50}{\cot25}$$ ...
7
votes
2answers
174 views

Prove $\tan 54^\circ=\frac{\sin24^\circ}{1-\sqrt{3}\sin24^\circ}$

How to prove this identity without using the actual values of $\tan54^\circ$ and $\sin24^\circ$ $$\tan 54^\circ=\dfrac{\sin24^\circ}{1-\sqrt{3}\sin24^\circ}$$ Edit: I still don't get it, I am ...
0
votes
1answer
61 views

Find the exact values without a calculator: (a) $\tan \frac{11\pi }6$ (b) $\sec \frac{-3\pi}4$ (c) $\cot \frac{-5 \pi}3$

Okay I know the unit circle back and forth, but I get confused when I am asked to find answers that do not refer to sine and cosine. For example, I am ask to evaluate $\tan \frac{11\pi }6$. Since ...
1
vote
3answers
28 views

Understanding trigonometric identities

Can someone help me understand trigonometric identities? For example, it is known that $\cos(90-\theta)$ is equal to $\sin \theta$, and vice versa. But why? Is it something to do with the unit circle? ...
0
votes
2answers
48 views

finding the value of $Z+Z^{2}+Z^{3}… $ if…

If $ Z+Z^{-1} = 2 \cos 5$ then what's the value of $Z+Z^{2}+Z^{3}.... ......Z^{63}$. I wanted to to solve this with the value of $Z$. But may be the value of $Z$ is complex. Now it's quite impossible ...
0
votes
3answers
41 views

Trigonometric Identities involving fractions

The question is to simplify: However, when I do that I end up with: $\frac{\cos\theta}{\frac{1}{\cos\theta}}$ Now, I don't know how to deal with these types of fractions. I have not encountered ...
1
vote
4answers
78 views

What does "sin$\theta > 0$ mean here?

The question is: If $\tan$ $\theta$ = -$\frac{8}{15}$, and $\sin$ $\theta$ > $0$, find $\cos$ $\theta$. What I did was draw a triangle on the unit circle with sides 8, 15 and therefore ...
-4
votes
1answer
32 views

Trigonometric Substitution LHS and RHS

Show by substitution into LHS and RHS that each trigonometric identity is satisfied by the given values of the angles. $(a)$ Show that $\sin2\theta=2\sin\theta\cos\theta$, when $\theta=150^\circ$. ...
0
votes
2answers
42 views

Exact value of a trigonometric ratio

I was asked to find the exact value of $\tan 240^\circ$. On my calculator, I type $\tan 240^\circ$, and then square the value to get a final answer of $\sqrt3$. However, the textbook answer says the ...
1
vote
2answers
27 views

Simplifying difference trig expression

Rewrite the following expression as a simplified expression containing one term: $$\cos (\frac{\pi}{3}+\varphi) \cos (\frac{\pi}{3}-\varphi) - \sin (\frac{\pi}{3}+\varphi) \sin ...
3
votes
1answer
61 views

How to solve the trigonometric equation $\cos (\pi\theta/\beta) - \cos(2\pi\theta/\beta)=0$?

I have a question regarding a problem I've been attempting to solve. It is an acceleration equation: $$a = ...
3
votes
1answer
42 views

Finding exact values of trig functions

Find exact value of each trigonometric function of $\theta$ if $\tan\theta=-1/5$ and $\sec \theta >0$ I know that $\cot \theta=-5,$ right? Secant and cosine are positive in the fourth ...
0
votes
4answers
51 views

Rewriting trigonometric expression in terms of $\cot x$

Rewrite the following expression in terms of $\cot x$: $$\frac{1}{1-\cos x}-\frac{\cos x}{1+\cos x}$$ I usually show my work on this site but I'm really lost about this problem. Any help ...
1
vote
2answers
37 views

Using sketch to find exact value of trigonometric expression

Use sketch to find exact value of $\tan (\cos^{-1}\dfrac{5}{13})$ I drew a right triangle with angle $\theta$ and sides $12,5,3.$ If $\cos \theta=\frac{5}{13},$ then $\sin \theta = \frac{12}{13}$ ...
2
votes
1answer
60 views

Help needed in verifying a trigonometric identity

I have the following identity: $$32\sin^{2}\left(\theta\right)\cos^{4}\left(\theta\right) =2 + \cos\left(2\theta\right) - 2\cos\left(4\theta\right) -\cos\left(6\theta\right) $$ I've tried ...