# Tagged Questions

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

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### Are there complex numbers whose sines are zero?

I recently learned that $\sin(z)$ has an extension into the complex plane, namely: $$\frac{e^{iz}-e^{-iz}}{2i}$$ Is there any complex number $z=a+bi$, with $b≠0$ such that $\sin(z)=0$ ? I am ...
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### Translate Pitch and Roll Angles of Object to those at different Yaw

I have been trying to find a method to translate the pitch and roll angles of one object to those of another connected object at a different yaw - i.e I have an IMU mounted on a quadcopter frame and a ...
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### Finding the solutions of $\sin\left( x - \frac{\pi}{4} \right) = \sin\left( 3x + \frac{\pi}{4} \right)$

Find all the solutions for $x$ in the following equality. $$\sin\left( x - \frac{\pi}{4} \right) = \sin\left( 3x + \frac{\pi}{4} \right)$$ I tried using the following formulas for both ...
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### Find $a$, $b$ and $c$. [on hold]

As title said, How to find angles $a$, $b$ and $c$? Thanks in advance!
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### Is there no formula for $\cos(x^2)$?

I was wondering if there was a "formula" or an "identity" for $\cos(x^2)$, as there is for $\cos(2x)$. My question is closely related to this one, which was only asking for $\cos(ab)$. For instance ...
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### Using derivatives to get some trigonometric identities

Is there a way of using derivatives to get some trigonometric identities in a straight-forward fashion? I use to forget them, so that would help me a lot... For example, since when we get the ...
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### how **(1)** $(2n-1)\pi/2 + (-1)^n\pi/3$ and **(2)** $2n\pi±\pi/6$ indicates the same angle?

I'm learning Trigonometry right now with myself and at current about General solution. I have a question in my book which I don't understand how to proof. The question is Show that the two angles are ...
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### Equetion of difference sinus and cosinus functions

Hi i have question i have something like this: $2 \sin 5t - 5 \cos 5t = A \sin(5t + \varphi)$ The main question is : Is there any formulas or something to change left side of "$=$" to look similar ...
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### what functions/formula gives me linear progression from 90 -> 180/-180 -> -90

in my programming code the angles of a camera goes from TOP 90 to MIDDLE 180 to -180 to BOTTOM -90 what formula would give me a linear progression between those values? i need to move the camera up ...
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### Trigonometric Equation Simplification

$$3\sin x + 4\cos x = 2$$ To solve an equation like the one above, we were taught to use the double angle identity formula to get two equations in the form of $R\cos\alpha = y$ where $R$ is a ...
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### Find the ratios of the sides of a triangle

If the perimeter of a the right-angle triangle is six times its smallest side, find the ratios of the three sides. I tried solving it by using the normal area and volume.
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### What is the third positive number starting from zero that will satisfy $\cos 6x = \cos x$? [on hold]

What is the third positive number starting from zero that will satisfy $\cos 6x = \cos x$? I need help on this one. I don't know how to approach this problem.
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### Compound angle formula

I understand how to use the compound angle formula when solving $\sin(\pi/12)$. However I dont understand how I can use a compound angle formula to show $$\arctan(3)-\arctan(1/2)=\pi/4$$ Thankyou Any ...
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### How to prove that $\lim\limits_{x\to0}\frac{\sin x}x=1$?

How can one prove the statement $$\lim\limits_{x\to 0}\frac{\sin x}x=1$$ without using the Taylor series of $\sin$, $\cos$ and $\tan$? Best would be a geometrical solution. This is homework. In my ...
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### Proving a trigonometric identity

How can one prove the validity of this trigonometric identity? $$2\arccos\sqrt{x} = \frac{\pi }{2}-\arcsin(2x-1)$$