# Tagged Questions

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### 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 $\dfrac{\tan(x+y)-\tan x}{1+\tan(x+y)\tan x}=\tan y$ $$=\frac{\tan x+\tan y-\tan x+\tan^2x\tan y}{1-\tan x\tan y+\tan^2x+\tan x\tan y}$$ ...
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### 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 ...
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### 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 ...
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### $m\cos^2{\theta} + n\sin^2{\theta} < l \implies \sqrt{m}\cos^2{\theta} + \sqrt{n}\sin^2{\theta} < \sqrt{l}$

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 $m, n, l >0$.
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### 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 $x=\tan^2t$, $y=\sec t$.
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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 = $0$?
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### 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, ...
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 $\cos(2x) = ... 3answers 102 views ### Problems with trigonometry getting the power of this complex expression I'm here because I can't finish this problem, that comes from a Russian book: Calculate$z^{40}$where$z = \dfrac{1+i\sqrt{3}}{1-i}$Here$i=\sqrt{-1}$. All I know right now is I need to use ... 4answers 41 views ### Calculating the angle for a path between two nodes in a graph I want to (programatically) draw an edge between two nodes in a graph, starting on the outside of the nodes. Below is an illustration of what I'm (poorly) trying to describe: I have the$(x,y)$... 3answers 38 views ###$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, ... 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 ... 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:$a/\sin\theta = c/\sin C$... 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 ... 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 ... 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 ... 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 ... 1answer 36 views ### Trigonometric Identity problem involving cot Simplify$\displaystyle\frac{\cot25 + \tan65}{\cot25}$My attempt is: $$\frac{\cot25 + \tan65}{\cot25}=\frac{\cot25 + \cot(90 - 65)}{\cot25}=\frac{\cot25 + \cot25}{\cot25}= \frac{\cot50}{\cot25}$$ ... 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 ... 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 ... 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? ... 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$is complex. Now it's quite impossible ... 3answers 41 views ### Trigonometric Identities involving fractions The question is to simplify: However, when I do that I end up with:$\frac{\cos\theta}{\frac{1}{\cos\theta}}$Now, I don't know how to deal with these types of fractions. I have not encountered ... 4answers 78 views ### What does "sin$\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 ... 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$\theta=150^\circ$. ... 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 ... 2answers 27 views ### Simplifying difference trig expression Rewrite the following expression as a simplified expression containing one term: $$\cos (\frac{\pi}{3}+\varphi) \cos (\frac{\pi}{3}-\varphi) - \sin (\frac{\pi}{3}+\varphi) \sin ... 1answer 61 views ### How to solve the trigonometric equation \cos (\pi\theta/\beta) - \cos(2\pi\theta/\beta)=0? I have a question regarding a problem I've been attempting to solve. It is an acceleration equation:$$a = ... 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 ... 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 ... 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}\$ ...
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 ...