# Tagged Questions

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### $2 \cos^2 x − 2 \cos x− 1 = 0$ Find the solutions if 0° ≤ x < 360°

Find the solutions of $$2 \cos^2 x − 2 \cos x− 1 = 0$$ for all $0° ≤ x < 360°$. For $0° ≤ x < 360°$, I'm getting $x=111.5°$ and $x=248.5°$. Is this correct? Thanks!
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### Polar graph question

Can you only graph periodic functions using polar graphing? I'm not really understanding this I guess. It you are to get all of the x and y values on a finite graph, then the original must be ...
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### 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 ...
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### Prove that $\frac{\sin^2 (2\alpha)}{\sin^2 (\alpha)}=4-4\sin^2 (\alpha)$.

$$\frac{\sin^2 (2\alpha)}{\sin^2 (\alpha)}=4-4\sin^2 (\alpha)$$ I have to solve the left hand side to equal the right hand side.
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### How do I get an exact value for the trigonometric expression?

I'm trying find an exact value for $$\cos\left(\frac{1}{3}\arctan\left(\frac{-10}{9\sqrt{3}}\right)\right)$$ Evaluating $\cos(\arctan(\frac{-10}{9\sqrt{3}}))$ is straighforward, but I'm having ...
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### How do I prove this trigonmetric identity?

I need to prove that the following identity is true: $$\frac{\cos^2x-\sin^2x}{1-\tan^2x}=\cos^2x$$ This isn't homework; just a practice exercise. But I keep getting stuck! Thanks much.
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### Partial fraction decomposition of $\frac{1}{x^{2n}+a^{2n}}$

I came across a formula for the partial fraction decomposition of $\displaystyle \frac{1}{x^{2n}+a^{2n}}$. It seems correct (at least for $n=1,2$, and $3$). But how is it derived? ...
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### factoring trig functions

I'm having an issue with factoring trig functions. For example the following: $$x^2 \ cos(2x) + 2x \ sin(2x) \\$$ I thought it was $$x(x\ cos(2x) + 2 \ sin(2x)) \\$$ But this is what my books ...
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### Meaning of “edge of the building”?

I'm hoping someone can tell me what they mean "edge of the building" in the following word problem: ...
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### Approximation to $\sqrt{\cos(\theta)}$?

I have this formula, (it is just the law of cosines angle formula): $$d = \sqrt{a^2 + b^2 - 2ab \ cos(\theta)}$$ Here is my issue. I am wondering if there is a way to 'extract' the $cos$ term. My ...
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### Trigonometry inside a trapezium

I have the following image, and it's asked to find the values of $X$ and $Y$. I've managed to find it using the this idea: Divide the image in two right triangles and let's call the height of the ...
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### A trigonometric equation with many cases

I have to solve the equation $4\cos^m(x)+3\sin^n(x)=5$ where $m$ and $n$ are non-negative integers. So here comes my question: The case $m=n=0$ is trivial. The case $m=n=1$ is easy to solve. We ...
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### Trigonometric eq.

The equation $3\sin(x)+4\cos(x)=5$ is well-known. The equation $3\sin^m(x)+4\cos^n(x)=5$ where $m$ and $n$ are non-negative integers is much more interesting.. I would like to see a nice, elementary ...
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### How do I solve for the height of a triangle?

The basic triangle looks something like this: How do I solve for $h$? As an example, in one problem I was given $b = 45, c = 42, \angle C = 38^\circ$ I understand how $h$ divides $\triangle ABC$ ...
The angular displacement $\theta$ of a certain pendulum bob in terms of its initial displacement $\theta_0$ is $$\theta=\theta_0 \cos wt\ .$$ If $w=3.00$ (rad/s) and $\theta_0=\pi/30$ rad, draw two ...