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

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1
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2answers
26 views

Calculating appearance of size of object at given distance

Here's the problem I'd like to solve. If I'm 1 ft away from a computer screen and a word on the screen appears a certain size, is there an equation or calculation that will tell me how big that ...
0
votes
1answer
36 views

Find the value of $\sin\frac{19 π}{2}$ using the addition and subtraction trigonometry formulas

The formula is $\displaystyle\sin(s-t)= \sin(s)\cos(t) - \cos(s)\sin(t)$ $$\sin \frac{19 π}{2}=\sin \left(\frac{21 π}{2} - \frac{2π}{2}\right)$$ I am not sure I know how to convert radians. I would ...
0
votes
5answers
70 views

Solve $x$ for equation : $\sin^2(x) - \cos(x) - 1 = 0$

I am trying to solve $x$ for $\sin^2(x) - \cos(x) - 1 = 0$, for $0°\leqslant x \lt 360°$. I have the key with the answer $0°$ but have been unable to confirm this using Wolfram Alpha (I assume I ...
1
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1answer
12 views

Inverse Laplace transform, none factorable denominator

I am really stumpted on this problem and can't seem to figure out where to go from where I am. Can anyone give me some advice or hint where I should do next? Here is the problem: ...
1
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3answers
53 views

Prove this trig identity

$$\sin^2(x) - \cos^2(x) - \tan^2(x) = \frac{2\sin^2(x) - 2\sin^4(x) - 1 }{ 1-\sin^2(x)}.$$ I tried this but I can't figure out how they got $-2\sin^4(x)$.
0
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0answers
35 views

Worded trig question

From the top of a vertical cliff 125m high, the angle of depression to the top of a ship is 3.5°. If the ship is 1800m from the base of the cliff, determine the height of the ship above the water. I ...
2
votes
1answer
36 views

Parametric & Trigonometry

$$x=7\sin(t)+\sin(7t)$$ $$y=7\cos(t)+\cos(7t)$$ How would I solve this one out? I have to simplify the two enough to graph it. I squaring the two and adding them together, but I hit a roadblock: ...
3
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1answer
45 views

For which angles is inequality true

My problem is from Israel Gelfand's Trigonometry textbook. Page 48. Exercise 6: a) For which angles $\alpha$ is $\sin^4\alpha-\cos^4\alpha > \sin^2\alpha-\cos^2\alpha$ ? b) For which angles ...
20
votes
5answers
4k views

Why is $\sin(d\Phi) = d\Phi$ where $d\Phi$ is very small?

I haven't touched Physics and Math (especially continuous Math) for a long time, so please bear with me. In essence, I'm going over a few Physics lectures, one which tries to calculate the Force ...
0
votes
2answers
40 views

Trigonometric equation with generalized solution

The equation $$\cot A - \tan A=2$$ Find the generalized form of $A$ I got the answer and the answer came $$\tan A=(2^{1/2})-1 \text{ and } -2^{1/2}-1$$ Now how to write the generalized form j ...
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0answers
22 views

Use an addition or subtraction formula to write the expression as a trigonometric function of one number: [closed]

$\cos\frac{3\pi}{7}\cos\frac{2\pi}{21}+\sin\frac{3\pi}{7}\sin\frac{2\pi}{21}=\cos\frac{\pi}{A}=\frac{B}{2}.$ Find $A$ and $B.$
1
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5answers
39 views

Verify algebraically that the equation $\frac{\cos(x)}{\sec(x)\sin(x)}=\csc(x)-\sin(x)$ is an identity

I am stuck when I get to this point $\frac{\cos^2(x)}{\sin(x)}$. Am I on the right track? Verify algebraically that the equation is an identity: ...
1
vote
3answers
29 views

Related Rates Ladder Problem with Angles

The problem is as follows: A 13-foot ladder leans against the side of a building, forming an angle θ with the ground. Given that the foot of the ladder is being pulled away from the building at the ...
1
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3answers
106 views

Evaluate $\int \frac{\tan^3x+\tan x}{\tan^3x+3 \tan^2x+2 \tan x+6} dx$

$$\int \frac{\tan^3x+\tan x}{\tan^3x+3 \tan^2x+2 \tan x+6} dx$$ My approaches so far has been using substitution with $\tan x = t$ and $\tan \frac x2 = t$ but the calculations has been harder than I ...
1
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0answers
18 views

Laplace transform of Differential Equation with a piecewise function

Hi I have this question and I am horribly stuck at one part and I cant seem to figure out if i did something wrong so any advice or help would be greatly apprecaited. Here is the question: ...
0
votes
0answers
11 views

Finding Opening Angles (in an Algorithm)

I seem to be spending far too long on what I thought was an easy task. I have a set of polar points (I start with the XY coords). The angles are measured from the vertical, in a clockwise manner, as ...
0
votes
4answers
66 views

Derivative with respect of a function

i have a function of two variables: $f(\theta,\phi) = \theta \sin(\phi)$ and i have to differentiate $f(\theta,\phi)$ with respect to: $1 - 0.5\theta^2$ That is: ...
1
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1answer
32 views

Solving right triangle given the area and one angle

Given right angle triangle $ACB$ (C is the right angle) has an area of 224 $mm^2$, what is the length of leg b if angle A equals 31.7deg? Here's the scenario: I have one right triangle completely ...
0
votes
1answer
43 views

Trigonometrics involving tangent [closed]

It is possible to solve $\tan(120^\circ)$ using calculator. However, when it comes to $\tan(90^\circ+30^\circ)$, the calculator just showed Math Error. Why?
1
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1answer
49 views

Rewriting a double integral with complex exponential function

Why can we write $$ \begin{align} I_T &= \int_\mathbb{R}\int_{-T}^{T}\frac{e^{-ita}-e^{-itb}}{it}e^{itx}dtdF(x)\\ &= \int_\mathbb{R}\left[\int_{-T}^{T}\frac{\sin(t(x-a))}{t}dt - ...
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2answers
32 views

Find the exact value of the expression [closed]

tan[arcsin(-10/11)] And it says Enter your answer in radians.
0
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2answers
39 views

Problem related to Mean Value Theorem

I found out a question that I can't figure out a way to solve it. Plz can anyone help me. Question is, Prove that $\exists\,C\in(0,\pi/4)\,\mathrm{s.t.}\,\tan(\pi/4+C)=3/C$ I know this should be ...
-1
votes
2answers
36 views

Trig Question, Please help.

Use the given value and the trigonometric identities to find the remaining trigonometric functions of the angle. $\cot \theta = −4$, $\sin \theta > 0$ Then it asks me to find: $ \sin(\theta) $, ...
0
votes
0answers
24 views

Looking for a method to solve simple trigonometric equations

Assume that $N$, $q$, $k_1$ and $k_2$ are integers such that $N>1$, $0\leq k_1<k_2<N$ and $q\geq 3$. Is there a method to solve the following trigonometric equation: $$ \sin\big(\frac{\pi ...
2
votes
1answer
28 views

Dirac Delta Function, Initial Value Problem

Hi I finished this IVP but I cant seem to get the right answer can someone give me some advice as to where I went wrong and point me in the right direction as to how to fix it. Here is the problem and ...
1
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0answers
38 views

find the angles of a given vector sum

Assume you have n vectors in 2D space, with different fixed magnitudes $l_i$. The problem is to find the angle of each vector such that vector sum is a specific vector. That is, $\sum l_i \cos ...
10
votes
2answers
269 views
+50

A closed form for $\int_{0}^{\pi/2} x^3 \ln^3(2 \cos x)\:\mathrm{d}x$

We already know that \begin{align} \displaystyle & \int_{0}^{\pi/2} x \ln(2 \cos x)\:\mathrm{d}x = -\frac{7}{16} \zeta(3), \\\\ & \int_{0}^{\pi/2} x^2 \ln^2(2 \cos x)\:\mathrm{d}x = ...
2
votes
3answers
63 views

Using the Chain Rule to prove trig derivatives

I'm having trouble with this problem, I'm not sure how to tackle it and I was wondering if somebody could set me on the right path. The problem is as follows: Use the Chain Rule to show that if ...
3
votes
4answers
50 views

Prove trigonometry identity for $secx\quad -sinx$

I'm trying to prove this equality but I' stuck at the second step. Please give me some hints or other ways to proceed. $\frac { { tan }^{ 2 }x\quad +\quad { cos }^{ 2 }x }{ sinx\quad +\quad secx } ...
6
votes
1answer
84 views

Evaluate: $I = \int^{\pi/2}_0 (\sqrt{\sin x}+\sqrt{\cos x})^{-4}dx$

Evaluate : $$I = \int_{0}^{\Large\frac\pi2} (\sqrt{\sin x}+\sqrt{\cos x})^{-4}\ dx$$ Attempt : \begin{align} I&=\int_{0}^{\Large\frac\pi2} (\sqrt{\sin x}+\sqrt{\cos x})^{-4}\ dx\\ ...
3
votes
2answers
67 views

Integration practice of $\int \frac{\sqrt{25-y^2}}{y}dy$

I need to solve $\int \frac{\sqrt{25-y^2}}{y}dy$. I originally thought IBP, but that led to a very large and confusing algebra problem. Then I started to look at the $\sqrt{25-y^2}$ and started to ...
0
votes
1answer
63 views

How to solve $\sin{x}=c \,x$?

I'm trying to find $x$ in the following equation, where $c$ is a known constant: $\sin{x}= c \,x$ Any help is appreciated.
0
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2answers
33 views

solving more than 2 vector sum [closed]

Assume you have $n$ vectors in 2D space, with different fixed magnitudes $l_i$. The problem is to find the angle of each vector such that vector sum is a specific vector. That is, ...
0
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2answers
50 views

Prove trigonometry identity for $\sin A+\cos A$

I’ve been struggling in proving this identity for hours (yes, shame on me), but I can’t see any light. $\frac { \cos(A) }{ 1-\tan(A) } +\frac { \sin(A) }{ 1-\cot(A) } =\sin(A)+\cos(A)$ I've been ...
0
votes
2answers
27 views

Applying the cosine even identity to the cosine difference identity

I'm slightly confused over what happens when you're applying cosine's "even identities" to the difference identity. Here's how I go about, please tell correct me as I feel i'm going wrong somewhere. ...
3
votes
0answers
66 views

How to solve this problem 4

Question $1$: Is $\frac{1}{\pi}\arccos\left(\frac{{\sqrt{2*\sqrt{2*\sqrt{2}*...n}}}}{2}\right)$ always a rational number when each$*$ is either $+$ or $-$ and $n$ may or may not be infinite? ...
0
votes
0answers
28 views

Similar triangle, Quick question (Thick Lens Formula)

http://www.panohelp.com/thinlensformula.html On the right hand side, f is defined as focus of the lens, i understand why the image distance is (f + fm). However i have spent an afternoon and could ...
2
votes
1answer
39 views

How to solve this differential equation sinusoidal?

I can't find how to separate variables. $$y= \sin(xy')$$
1
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2answers
29 views

Simple Trigonometric Equation

I am asked to solve the trigonometric equation $2cos \theta = \sqrt 3$ I rearrange it to $cos\theta = \frac{\sqrt3}{2}$ Now, at this point I am not sure what to do? Can someone describe to me the ...
0
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3answers
53 views

Prove that $n\sin\frac{2\pi}{n}-\frac{1}{4}n\sin\frac{4\pi}{n}>\pi$ (corrected inequation)

Prove that Prove that $n\sin\frac{2\pi}{n}-\frac{1}{4}n\sin\frac{4\pi}{n}>\pi$ algebraically or geometrically. $n\sin\frac{2\pi}{n}-n\sin\frac{\pi}{n}$ means the area of a regular n-gon + the area ...
0
votes
1answer
40 views

Calculate length of radial intersecting a rectangle

In a rectangle like below, I need to calculate the length of any radial, from the center of the rectangle to where it intersects with the edge of the rectangle. Further, the angle of the radial is ...
1
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1answer
92 views

How Can I figure out when cosine = $\frac{2}{\pi}$?

So I'm doing Mean Value theorem homework which states $$f'(c)=\frac{f(b)-f(a)}{b-a}$$ So I am trying to find $c$ for $f(x)=\sin x$ over the interval $[0,\frac{\pi}{2}]$. So using the Mean Value ...
1
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3answers
58 views

solve $3\sin\theta+4\cos\theta=0$

Solve for $0 < \theta < 360$ Question $3 \sin \theta + 4 \cos \theta = 0$ Please help. I really can't figure this out Thanks :) What I have tried I tried using the a $\sin \theta + b ...
1
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5answers
38 views

$12\frac{\sin 45^\circ}{\sin 60^\circ}$ Need help breaking this down.

Otherwise known as $12\dfrac{\left(\frac{1}{\sqrt2}\right)}{\left(\frac{\sqrt3}{2}\right)}$ How do you simplify this multi level fractional radical expression into $4\sqrt{6}$.
0
votes
1answer
61 views

A few questions regarding the cosine difference identity

I've a few questions that stem from the proof given in my textbook regarding the cosine difference identity. The proof goes like this: Let $\alpha$ and $\beta$ be angles plotted in standard ...
0
votes
2answers
17 views

How to find all possible values of Ɵ for the equation cos4Ɵ=0 [closed]

I'm not exactly sure how I go about starting this equation.
2
votes
2answers
52 views

Find the derivative of $y=\cos(x) - 2\sin(x),$ when the gradient is $1$

I need to find the smallest positive value of $x$ for which the gradient of the curve has value 1. For this equation: $$ y =\cos(x)-2\sin(x) $$ The answer is 2.5c grad. The following is my ...
0
votes
1answer
50 views

Not understanding where the ratio comes from

I'm completely stumped at how they come up with the ratio AB : AC. Why not AC : AB? Where does this ratio come from? How can I get to this ratio myself? Please help.
-1
votes
1answer
48 views

Inverse Trigonometry proof

Please help me prove this equation as ive been trying for days and not able to solve the $\tan^{-1}( \cot^3 x)$ part. $$\tan^{-1}(\cot x)+\tan^{-1}(\cot^3 x)+\tan^{-1}(\frac{1}{2} \tan 2x)=0$$
2
votes
2answers
35 views

What is an algorithm for making text form a circle

Ok it's beyond the scope of this programming exercise, but I want to create a loop that will allow me to input any number of characters and the loop gets each character in the string and places it at ...