# Tagged Questions

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### Trigonometry Question - Tough one [on hold]

If in triangle ABC, sin A sin B sin C + cos A cos B = 1. Then find the value of sin C.
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### Trigonometry Question: find Value of…

Find value of $3 + \cos2x + \cos4x + \cos6x - 4\cos x\cos2x\cos3x$. I tried with $\cos A + \cos B$ identity but it was not simplifying.... Help..
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### Trigonometric functions of the acute angle

Find the other five trigonometric functions of the acute angle A, given that: \begin{align} &\text{a)}\ \ \sec A = 2 \\[15pt] &\text{b)}\ \ \cos A = \frac{m^2 - n^2}{m^2 + n^2} \end{align} ...
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### Solving equations with powers without logarithms

Im taking an introduction to logarithms. Of course a short review of exponentiation is inherent for a clear understanding of logarithms. I was asked to find, for example, $27^x = 3$. (without the use ...
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### Simple Trig Question / Introduction to Vectors Question

Sorry this is such a simple question; I'm just struggling a little with my trigonometry homework. An example question: "A ship sails due north (relative to the current) with a speed of 20 knots. The ...
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### Taking the sin of arccos

When solving for the value of x in the equation $$\sin^{-1}{(\sqrt{2x})}=\cos^{-1}(\sqrt{x})$$ one would take the sin of both sides of the equation cancelling out the arcsin leaving ...
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### Sum of this series

$$\mbox{How do I find the sum of this series}\quad \sum_{n=0}^{\infty}{\sin^{3}\left(3^{n}\right) \over 3^{n}}\ {\large ?}$$ Hints in the right direction would be appreciated.
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### Evaluating a limit involving trigonometry

I really thank you for your answers to my first question--I could easily solve first problem and a few more ones without another question. But a while later I got another one while studying, then I ...
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### How to solve: $\cos^2x + \sin x = 1$

$\cos^2x + \sin x = 1$ How to solve for $x$?
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### Finding a point in a parallelogram

QUESTION: Find the point$(x,y)$ so that $(x,y)$ is in the first quadrant and $(x,y),(1,2),(4,10)$ and $(2,6)$ are vertices of a parallelogram.. I find this question very difficult.. Thanks...
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### Express $\sin 3\theta$ and $\cos 3\theta$ as functions of $\sin \theta$ and $\cos \theta$ using Euler's identity

Using Euler's identity ($e^{in\theta}=\cos n\theta+i \sin n\theta$), express $\sin 3\theta$ and $\cos 3\theta$ as functions of $\sin \theta$ and $\cos \theta$. Any ideas?
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### Find the exact value of $\sin (\theta)$ and $\cos (\theta)$ when $\tan (\theta)=\frac{12}{5}$

So I've been asked to find $\sin(\theta)$ and $\cos(\theta)$ when $\tan(\theta)=\cfrac{12}{5}$; my question is if $\tan (\theta)=\cfrac{\sin (\theta) }{\cos (\theta)}$ does this mean that because ...
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### Finding an area of a triangle inside of a triangle, given certain areas of other triangles, and area ratios.

I'm studying for the Waterloo Math Contest (Galois, Gr. 10) taking place in April of 2015 and I am preparing by looking at previous problems and solving them. This is question 4(c) on the 2010 Galois ...
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### 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 ...
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### How to find length of the sides of a triangle given the ratio of the sines of the sides?

Consider $\triangle ABC$. Let $\dfrac{\sin A}{\sin B} = \dfrac56$ and $\dfrac{\sin B}{\sin C} = \dfrac45$. Find $\dfrac{\vert AC\vert\cdot \vert AB\vert}{\vert BC\vert}$. If there is no definite ...
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### $f(x)=sec(x)$ inequality inconsistency\trouble

I'm currently attempting to find the range of $f(x)=\sec(x)$ by considering $\cos(x)$ in the intervals of $0<\cos(x)\leqslant 1$ and $-1\leqslant \cos(x)<0$ (as $\sec(x)$ is undefined for ...
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### Calculate $\frac{2\cos40^\circ-\cos20^\circ}{\sin20^\circ}$

I am trying to solve this task i.e. calculate this expression without using calculator, in terms of known values for angles such as 30,60,90,180 degrees :). ...
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### 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 ...
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### Value of $\frac{\cos 45}{\sec 30 + \operatorname{cosec} 30}$

I just put the values from the trignometric table to solve, but the answer is different in the answer book. $$\frac{\cos 45}{\sec 30 + \operatorname{cosec} 30}$$
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### Finding all the values of $\theta$ for which $\tan(\theta)=\sqrt3$; problem with understanding.

My textbook has a section where it defines $\tan(\theta)$ as the following: "For acute angles $\theta$, $\tan(\theta)$ is the $y$-coordinate of the point on the terminal side of $\theta$ which lies on ...
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### integration by parts of trig functions

Can anyone help me with this integral? $\int{x^3 \sin(x^4) dx}$ I set $u=x^3$, and I let $v=-\cos(x^4)$, so that $\frac{dv}{dx}=\sin(x^4)$ I tried using integration by parts, but, whenever I come ...
If $$m\tan(X - 30) = n \tan(X + 120)\ ,$$ then find $\cos 2X$ in terms of $m$ and $n$.
### A question about the definition of the circular function $\tan(\theta)$
The circular function $\tan(\theta)$ is defined as $\tan (\theta)=\frac{\sin (\theta)}{\cos (\theta)}$. If we look at this in the context of the Unit Circle: From this picture it can be seen that ...