# Tagged Questions

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### Finding the area under an arcsecant curve?

this question was in my revision, and I've been having a little bit of trouble with it. "Find the volume of the solid formed if the curve $y=sec^{-1}x$ is rotated about the x-axis from x=0 to x=0.5, ...
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### Solve $\sin x - \cos x = -1$ for the interval $(0, 2\pi)$

We have an exam in $3$ hours and I need help how to solve such trigonometric equations for intervals. How to solve $$\sin x - \cos x = -1$$ for the interval $(0, 2\pi)$.
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### Trigonometric Substitution

Question: Use the substitution x=3sin(t) to evaluate the integral of I started by making a right triangle and solving for sin(t) and cos(t). sin(t)=x/3 and cos(t)=(sqrt(9-x^2))/3 Then, I solved ...
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### show that trigonometry inequality holds

show that trigonometry inequality holds for $\displaystyle x\in\left(0, \frac{\pi}{12}\right)$ $$\frac{\cos{x}}{\sin^2{x}(\cos{x}-\sin{x})}>8$$ I tried to swich all to sines but it didn't help ...
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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 $\triangle ABC$ ...
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### Simplifying Trig Identities

I feel like this problem is simple, but I am having a hard time wrapping my head around it. $$\dfrac{1}{sin^2(x)}+ \dfrac{sec^2(x)}{tan^2(x)}$$ Any suggestions?
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### Finding sides of a triangle. Why does this work?

My Question: For the following problem, I know how to solve it, but I don't know why one of the steps works in solving it. That is the part where you use the Pythagorean theorem: $x^2 + x^2 = 25^2$ ...
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### If $x+y+z=xyz$, find $\frac{3x-x^3}{1-3x^2}+\frac{3y-y^3}{1-3y^2}+\frac{3z-z^3}{1-3z^2}$

I found this question in a maths worksheet of trigonometry (kinda odd, right?), but I dont know how to figure it out. If $\displaystyle x+y+z=xyz$, find ...
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So we're learning trigonometry in school and I need a little help how to solve a equation. So I got the following equation: $\sin 3x * cos 3x = sin 2x$ so I used the formula $\sin a * cosb = ... 2answers 53 views ### Solving all possible triangles? So we're doing oblique triangles -- Law of Sines and all that good stuff =). I have a bunch of problems that ask you to solve for "all possible triangles that satisfy the given conditions". For ... 0answers 35 views ### trigonometry right angle Are these answers correct? Question #1 standing on one side of a court, a surveyor measures the angle to the top of the pole on the otherside of the court to be 23 (degrees). She backs up 45ft and ... 3answers 137 views ### How to solve simple trigonometry equation. So we are learning trigonometry in school and I would like to ask for a little help with these. I would really appreciate if somebody can explain me how I can solve such equations :)$\sin 3x \cdot ...
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At point, S, lies between a flagpole, 10 metres high, and a tower, 16 metres tall. Sophie is standing between the flagpole and the tower. From Sophie's position, the angle of elevation to the top of ...
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### Find the sum of these two angles.

I’m not sure if I’ve done this correctly. The answer I got is 12.5 degrees. Help would be much appreciated. This is how I got it: Found the missing side of CAD Found half of CAD Found GAF (I ...
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### Expressing $\cos(x)^6$ as a linear combination of $\cos(kx)$'s [closed]

Let $$(\cos^6(x)) = m\cos(6x)+n\cos(5x)+o\cos(4x)+p\cos(3x)+q\cos(2x)+r\cos(x)+a.$$ What is the value of $a$?
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### Rewrite $f(x) = 3 \sin (\pi x) + 3\sqrt{3} \cos (\pi x)$ in the form $f(x) = A \sin (Kx+D)$

I got a question like that said "Rewrite $f(x) = 3 \sin (\pi x) + 3\sqrt{3} \cos (\pi x)$ in the form $f(x) = A \sin (Kx+D)$". I'm inclined to think that since the periods are the same ($2$), that ...
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### What is wrong with this basic algebra/trig that I'm doing?

I have to solve for $x$: $e^{x\sqrt3}(3cos(3x)+\sqrt3sin(3x))=0$ So $3cos3x+\sqrt3sin3x=0$ Divide through by$cos3x$: $3+\sqrt3tan3x=0$ $tan3x=-\dfrac{3}{\sqrt3}$ $\therefore$ ...
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### Easy trigonometry question

$pqr$ is an equilateral triangle of side length $x$, and $ps$ is the perpendicular from $p$ to $qr$. $ps$ is produced to $t$ so that $pt$ = $x$. show that $pqt= 75°$. Any explanation is appreciated ...
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### Trig Problem. Find the angle.

I've spent hours on this problem now and I can't figure it out. :( I would very much appreciate some help. Thank you! A soccer field has a rectangular penalty area that measures 136 feet by 51 feet. ...
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### $\arcsin(\sin x)$ explanation?

First off, I know this is a duplicate of this question. I'm asking this because I still don't quite understand the answer given there. But first, some graphs! $y=\sin(x)$ $y=\arcsin(x)$ ...
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### Using De Moivre's Theorem to prove $\cos(3\theta) = 4\cos^3(\theta) - 3\cos(\theta)$ trig identity

I am stuck on trying to prove a trig identity using De Moivre's theorem. I have to prove, $$\cos(3\theta) = 4\cos^3(\theta) - 3\cos(\theta)$$ I am not sure where to even start, I broke the LHS down ...
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### How to calculate $\theta$ when we know $\tan \theta$.

Hej I'm having difficulties calculating the angle given the tangent. Example: In a homework assignement I'm to express a complex variable $z = \sqrt{3} -i$ in polar form. I know how to solve this ...
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### Simple trigonometric identity proof

How would you verify that this trigonometric equation is an identity? $$\sin^4x-\cos^4x=2\sin^2x-1?$$ The 4th powers are really throwing me off, and i'm still fairly new to this and there is no ...
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### Find the unit normal $N$

of ${\bf r}=14 \mathrm{e}^{-10 t}\cos(t){\bf i}+14 \mathrm{e}^{-10 t}\sin(t){\bf j}$ The answer should be in vector form. I can't find an easy way to do this. I end up with T being something ...
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### Proving An Equation [duplicate]

I have been revising basic compound angles and I am struggling to understand the following question from the examples I have previously studied on such topic. A first step, or point of ...