# Questions tagged [trigonometry]

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

20,145 questions
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### How do you solve the trigonometric equation $\sin(x)+x=9$?

How do you solve the trigonometric equation $\sin(x)+x=9$? More generally, how do you solve equations with both trigs and 'x's without graphing? And maybe I only want real number answers.
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### Linear Algebra - Linear Combination and Perpendicular to Triangle

I am working on my maths homework and encounter the following question which I have no clue to answer: Let A = (1, 1, 2), B = (-3, 1, 4), C = (-1, -1, 0) be points in space. Q1: Find all values x ...
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### Proving the identity $(\tan^2(x)+1)(\cos^2(-x)-1)=-\tan^2(x)$

Proving the trigonometric identity $(\tan{^2x}+1)(\cos{^2(-x)}-1)=-\tan{^2x}$ has been quite the challenge. I have so far attempted using simply the basic trigonometric identities based on the ...
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### Dot and Cross Products [on hold]

A mechanic applies a force of 42 Newtons straight down to a ratchet that is 0.59 meters long. What is the magnitude of the torque when the handle makes a 38° angle above the horizontal?
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### If $g'(0)>0$ write this expression $\lim\limits_{x \to 0} \frac{\sin(f(x))}{\sin(g(x))}$ using $f(0),f'(0)$ and $g(0)$.

If $g'(0)>0$ write this expression $\lim\limits_{x \to 0} \frac{\sin(f(x))}{\sin(g(x))}$ using $f(0),f'(0)$ and $g(0)$. This came up in my Analysis 1 exam, and i couldn't do it.
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### Degree between vector and point

I have a vector and a point $(x, y)$. The vector starts from $(0, 0)$ and goes to $(x_1, y_1)$. $x$, $y$, $x_1$, $y_1$ are known. How can I get the degree that vector should rotate clockwise to face ...
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### Figuring out positions of some points given other known points and angles between the known and unknown points

So the data in question is a set of points p which all have known positions in space, a set of points q which all have unknown ...
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### Circle with rotating line: Locate section on a tangent with known velocity in the section

I have a hard time phrasing this in the title but let me try to explain. You all probably know the demonstration graphics on the unit circle for trigonomic functions (look here for an example). Now I ...
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### The lengths of the sides of a triangle are $\sin\alpha$, $\cos\alpha$ and $\sqrt{(1+\sin\alpha\cos\alpha)}$…

The lengths of the sides of a triangle are $\sin\alpha$, $\cos\alpha$ and $\sqrt{(1+\sin\alpha\cos\alpha)}$, where $0^o < \alpha < 90^o$. The measure of its greatest angle is....... What I have ...
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### Find out the Coordinate of watch tower by coordinate geometry [on hold]

A watch tower will be built equidistant from both camp A and Camp B and near to Camp C. Find the coordinates of the watch tower. Camp A coordinate:(-600,200) ; Camp B coordinate: (300,500); Camp C ...
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### How can I write y in terms of x for the equation given below? [on hold]

Here is the equation: $x=\frac{1}{c}\cdot \text{tanh}^{-1}(y)-b\text{i}\cdot \text{tanh}^{-1}(b\text{i}\cdot y)$ $b$ and $c$ constants and $\text{i}$ for imaginary.
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### How was the system of $degrees$ devised? [on hold]

We are all familiar with the equivalence relationship between radians and degrees, $$1^c =\big(\frac{180}{\pi}\big)^o$$ I was wondering what else degrees are equivalent to. What is the basis of ...
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### Show that the expressions $\sin^{-1}(\frac{1}{\sqrt{x}})$ and $\frac{1}{\sqrt{x}}$ are the same for big values

How can you show that the expressions $\sin^{-1}(\frac{1}{\sqrt{x}})$ and $\frac{1}{\sqrt{x}}$ for big values are the same? The opposite side of a triangle is given with $1/\sqrt(x)$, the angle ...
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### How do you graph Sin of a double angle? [closed]

How does the double angle affect the sine graph, does it compress / stretch the graph, etc? eg. sin(2θ) = π/4
### Find the number of roots of the equation, $x^3 + x^2 +2x +\sin x = 0$ in $[-2\pi , 2\pi]$.
Find the number of roots of the equation, $$x^3 + x^2 +2x +\sin x = 0$$ in $[-2\pi , 2\pi]$. What I have tried: $$x^3 + x^2 +2x = -\sin x$$ $$x^2 +x +2 = \frac{-\sin x }{x}$$ (x + \frac{1}{2})^...