Tagged Questions
4
votes
2answers
68 views
Trigonometry Airplane question. Finding bearing and distance.
A little background(if you don't care for my story, skip straight to the question): I've missed a few lectures from my teacher because I fell ill. Since I have no information to work with other than ...
2
votes
4answers
43 views
How can I solve this Laws of Sines problem?
This is a homework question that was set by my teacher, but it's to see the topic our class should go over in revision, etc.
I have calculated $AB$ to be 5.26m for part (a). I simply used the law ...
0
votes
3answers
66 views
How to solve these?
Inverse Trigonometric Functions
They are incomplete and I don't know how to complete them.
Who can help me?
1st
$$
\int\frac 1{ x \sqrt{x^{6} - 4}}dx
$$
I tried with:
$$u = x^3 $$
$$du= 3x^2dx$$
...
5
votes
3answers
101 views
How can I prove that $\sin (10^\circ), \sin(1^\circ), \sin(2^\circ), \sin(3^\circ), \tan(10^\circ)$ are irrational
How can I prove that $\sin (10^\circ), \sin(1^\circ), \sin(2^\circ), \sin(3^\circ), \tan(10^\circ)$ are irrational?
My try:: Let $x = 10^\circ$, Then $3x = 30^\circ$
Now $\sin (3x) = \sin ...
0
votes
2answers
31 views
Trigonometrical Question
the question is solve the following equation in the interval
$$0<\theta\leq 360$$
$$\tan(\theta) = \tan(\theta)(2+3\sin(\theta))$$
I got 199.5 and 340.5 as my answers like so:
$\tan(\theta) = ...
2
votes
2answers
31 views
Integral of $\int \frac{\sin(x)dx}{3-\cos(x)}$
I am trying to solve this integral and I need your suggestions.
I don't know if its OK to set $3-\cos(x)$ as $t$ $\rightarrow dt = \sin(x)dx$ or just take $\cos(x)$ and set it as $t$
$$\int ...
1
vote
1answer
16 views
Find the equation of the hyperbola given foci and the minor axis
first time posting and using the site. I have a quick problem that I need some help with. I need to find the equation of a hyperbola given the foci and the length of the minor axis.
The foci ...
3
votes
3answers
102 views
How do you integrate the following trigonometric function involving sin and cos?
How do you integrate the following functions:
$$\int \left( \frac{\cos\theta}{1+\sin^2\theta} \right)^2 \, d\theta$$ and $$\int \left( \frac{\cos\theta}{1+\sin^2\theta} \right)^3 \, d\theta
$$
...
1
vote
1answer
25 views
Trigonometry Addition Thereom With Only one exact value?
Use the expression of $\sin(A+B)$ to evaluate $\sin 195$.
Do I use one exact value like $45+150$ or $60$ or is there another way?
0
votes
2answers
23 views
Trigonometry Addition Thereom
Using the expansion of
a. $\sin(𝐴+𝐵)$, prove that $\sin75°=\sqrt 6+\sqrt{24}$
b. $\sin(𝐴+𝐵)$, prove that $\tan75°=2+\sqrt 3$
Where to start? draw up triangle of sin 75? find other values? help ...
1
vote
1answer
64 views
Trigonometric equality $x = 99 \sin (\pi x)$
Find the number of real solutions of $\displaystyle x = 99 \sin (\pi x)$.
I am getting stuck in some trigonometric relations.
3
votes
2answers
57 views
Why do we need to find the intersection between these lines?
We have the functions
$$ x = -1 + 2 \cos(t)$$
$$ y = 3 + 2 \sin(t)$$
They give P's orbit
with $t$ on $\left[0, \dfrac{3}{2} \pi\right]$
Find (to 2 decimal places accurate) for which values of t ...
0
votes
1answer
40 views
Trigonometry - Addition and subtraction theorem
If $\theta$ and $\phi$ are angles between $0°$ and $90°$, and $\sin \theta=3/5$ and $\tan \phi=7/24$, find without the use of a calculator, the value of each of the following:
a. $\sin(\theta−\phi)$
...
1
vote
2answers
52 views
Determining pendulum rise using trigonometry
Everyone in my math class (including the teacher) is having problems with this trigonometry question:
I am assuming that you halve the pendulum and the bottom of the triangle would be $\frac{1.8}{2} ...
13
votes
3answers
219 views
Proving a trig infinite sum using integration
How can I prove the following using integration and elementary functions?
Prove that:
$$\sum_{n=1}^{\infty} \frac{\sin(n\theta)}{n} = \frac{\pi}{2} - \frac{\theta}{2}$$
$0 < \theta < 2\pi$
1
vote
6answers
86 views
A problem on range of a trigonometric function: what is the range of $\frac{\sqrt{3}\sin x}{2+\cos x}$?
What is the range of the function
$$\frac{\sqrt{3}\sin x}{2+\cos x}$$
3
votes
1answer
64 views
Find the maximum value of $T=\frac{2}{3}(\cos 2A-\cos 2B)-\tan\frac{C}{2}$
Let $ABC$ be a triangle. Find the maximum value of
$$T=\frac{2}{3}(\cos 2A-\cos 2B)-\tan\frac{C}{2}$$
Please give me some hints. I don't know where to start
Thanks
0
votes
0answers
35 views
Geometry question
The sides of a triangle are given to be $x^2+x+1$ , $2x+1$ and $x^2-1$. Then the largest of the three angles of the triangle is
a)75 degree
b)$\dfrac{x}{x+\pi}$
c)120 degree
d)135 degree
please ...
3
votes
1answer
101 views
How to simplify this trigonometric expression?
I was trying to solve a problem taken from an Physics Olympiad when I came across a curious and complex mathematical expression. I can not prove with what I know so far about mathematics, does could ...
0
votes
2answers
43 views
Can't solve this equation to $\phi$
It's the end of a Physics Problem.
2 Forces are equal, one is proportional to $\sin\phi$ the other to $$\frac{\cos\phi}{\text{distance}^2}$$
distance is proportional to $\sin\phi$ $$$$
I'm stuck at ...
1
vote
1answer
62 views
Differentiation of a natural log with fraction of trigonometric functions
I am starting with differenciation and I stumbled upon the following exercise:
Find $\frac{df(x)}{dx}$, where
$$f(x)=\ln \left({\cos x + \sin x \over \cos x - \sin x}\right).$$
So I applied the chain ...
8
votes
2answers
85 views
How to find the minimum of f(x)?
I need to find the minimum of $f(x)$ with
$$f(x)=(\sin(x)+\cos(x)+\tan(x)+\cot(x)+\sec(x)+\csc(x))^2$$
Could you help me with some clues?
0
votes
1answer
39 views
Maximum and minimum of $y = 4x-8*(\cos(x))$ between $-\pi$ and $\pi$
I have found that the maximum of this function is at $\pi$, where the function will equal $$4\pi+8,$$ which is approximately $20$. However, I tried to get the minimum value, and it was incorrect. The ...
0
votes
1answer
71 views
Upper and lower bound of $f(x)=(\tan x)^{\sin 2x}$ for $x \in (0, \frac{\pi}{2})$
Let define $f(x)=(\tan x)^{\sin 2x}$ for $x \in (0, \frac{\pi}{2})$
Please help me prove, that $f$ reaches its lower bound in only one point $x_1$ and reaches its upper bound $x_2$ also in only one ...
0
votes
1answer
50 views
Angle between 2 faces of a pyramid
The problem:
Given a pyramid with $P_0=(0,0,0)$, $P_1=(1,1,1)$, $P_2=(2,-1,2)$, $P_3=(3,0,1)$, find the angle between the $P_1P_2P_3$ face the $P_0P_1P_2$ face.
My idea for the solution is to ...
1
vote
2answers
58 views
Pythagorean Trig Identity
I'm about to teach basic Pythgorean trig identities and went through the textbook exercise but I'm stuck on one.
Show
$$\sec^2 A = \frac{ \mathrm{cosec} A}{ \mathrm{cosec} A - \sin A}$$
Can ...
3
votes
1answer
50 views
Trigonometry - Calculating the pyramid volume
The problem:
There be the points $P_0(0,0,0)$, $P_1(1,1,1)$, $P_2(2,-1,2)$ and $P_3(3,0,1)$. Calculate the volume of the pyramid.
Now I assumed the base of the pyramid is a triangle, with points ...
5
votes
2answers
178 views
$ \sin^{2000}{x}+\cos^{2000}{x} =1$ equation explanation
Solve the equation:
$$ \sin^{2000}{x}+\cos^{2000}{x} =1.$$
What I did:
$\sin^2{x} =1 \land \cos^2{x}=0$ when $x=\frac \pi2 + \pi k $
$\cos^2 {x} =1 \land \sin^2{x}=0$ when $x= \pi k$
I think ...
0
votes
0answers
25 views
vector proof, line of intersection of gutters
The gutters on two roofs meet at right angles and the roofs themselves make angles $a$ and $b$ with the horizontal. Show that the line of intersection of the roofs makes an angle with the horizontal ...
0
votes
2answers
60 views
A question on Trigonometry (bisector)
If two bisector of a triangular is equal, then it is Isosceles triangular.
2
votes
2answers
54 views
trigonometry equations
Take this question:
"We follow the tips of the hands of an old fashioned analog clock (360 degrees is 12 hours) . We take the clock and put it into an axis system. The origin (0,0) of the axis ...
0
votes
4answers
65 views
$\left(\frac{\sin(\frac{n\theta}{2})}{\sin(\frac{\theta}{2})}\right)^2=\left|\sum_{k=1}^{|n|}e^{ik\theta}\right|^2$
I'm having trouble proving $$\left(\frac{\sin(\frac{n\theta}{2})}{\sin(\frac{\theta}{2})}\right)^2=\left|\sum_{k=1}^{|n|}e^{ik\theta}\right|^2$$ where $n\in\mathbb{Z}$ and $\theta\in\mathbb{R}$. Can ...
0
votes
1answer
41 views
Solving for a variable
Assuming that we're given the function:
$$I_r(n) = \cos^{n-1}(\dfrac{45°}{n-1})$$
Which models the remaining intensity of a wave of light. n is how many polarizers must be placed (i.e. more ...
2
votes
1answer
54 views
Determining Approximate Solutions at Intervals - $\tan x$
I'm having a little trouble determining the solutions of:
$$\tan x - 5 = 0,~ \text{at the interval}~ x \in (0, Pi)$$
I figured that $tanx = 5$ and when you draw the graph you have to draw it ...
0
votes
2answers
225 views
Compound angle formulas
I need help understanding why how the textbook got a certain answer but I got a completly different answer.
The question was to apply a compound angle formula, and then determine and exact value for ...
1
vote
4answers
127 views
How to show that $ \frac{\cos x}{1 - \sin x} - \tan x = \sec x$?
Question is: verify the identity:
$$
\frac{\cos x}{1 - \sin x} - \tan x = \sec x.
$$
How do I show that the left side equals the right?
I changed $\tan x$ into $\sin x/\cos x$ but didn't get ...
2
votes
1answer
41 views
Trigonometry functions
How do I verify the following identity:
$$\frac{1-(\sin x - \cos x)^2}{\sin x} = 2\cos x$$
I have done simpler problems but got stuck with this one.
Please help.
Tony
3
votes
3answers
210 views
Express $\sin 4\theta$ by formulae involving $\sin$ and $\cos$ and its powers.
I have an assignment question that says "Express $\sin 4\theta$ by formulae involving $\sin$ and $\cos$ and its powers."
I'm told that $\sin 2\theta = 2 \sin\theta \cos\theta$ but I don't know how ...
1
vote
1answer
78 views
Finding $f'''(x)$ of $f(x)=\sin{\pi}x$
Finding $f'''(x)$ of $f(x)=\sin{\pi}x$.
First
$$f'(x)=\frac{d\sin{\pi}x}{d({\pi}x)}\frac{d({\pi}x)}{dx} ={\pi}\cos{\pi}x$$
Second
$$f''(x)=-{\pi^2}\sin{\pi}x$$
Third
$$f'''(x)= -{\pi^3}\cos ...
2
votes
2answers
62 views
Given $|\arctan x| \leq \frac{\pi}{4}$ prove that $|\sin x| \leq 2\cos x $
Can anyone give me a hint about how to approach this?
0
votes
1answer
61 views
radius = distance? arc length = height?
as the title said,
I have a little trouble to find which is radius and arc length
1)If a hill 2500 ft away subtend at 1.5 degree angle, how high is it?
my thinking:
it ask for the arc ...
1
vote
1answer
39 views
At what distance does a tree 24 ft tall subtend an angle of 10'?
At what distance does a tree 24 ft tall subtend an angle of 10'?
this is what I got,
given formula: d = rθ
θ = 1/60 degree * 3.14/180 degree = 2.9 x 10^-4 or 0.00029
d = rθ = (24)(.00029) = ...
0
votes
4answers
77 views
Make use of trigonometric identities to get the value of all 6 trigonometric functions of 165 degrees
Use trigonometric identities to get the value of all 6 trigonometric functions of 165 degrees.
-2
votes
1answer
47 views
maths help stuck on these ones 2
6) A platform which starts fifteen metres above the ground & goes up & down.
The distance = s metres of the platform above the ground, t = seconds after the ride starts, can be modelled by the ...
1
vote
2answers
58 views
Find all $ x \in [0^{\circ},360^{\circ}] $ for which $ |2 \sin(x) − 5| < 4 $.
I have no idea how to solve this:
Find all $ 0 \leq x \leq 360^{\circ} $ satisfying $ |2 \sin(x) − 5| < 4 $.
1
vote
3answers
72 views
Real Solutions to the Equation
Can you please find all real solutions to the equation
$$2 + \sin (\theta )+\frac{(\sin(\theta))^2}{2}+ \cdots = 2$$
2
votes
1answer
100 views
Trigonometry and Geometry
I have no idea on how to solve this question so can someone please assist me. My son brought it from school and he is really struggling with the question.
Consider a triangle ABC with line segments ...
1
vote
1answer
70 views
Trigonometry Identities
Consider a collection of five points evenly spaced around a circle to form a regular
pentagon. Assume the figure is scaled so that the sides of the pentagon have length 1.
Question: Use Ptolemy’s ...
0
votes
2answers
65 views
Use the trigonometric identities to find functions, given $\cos x = 3/5$ and $x$ in quadrant $IV$.
Use the trigonometric identities to find $\sin x$, $\tan x,$ and $\cot (-x)$, given $\cos x = 3/5$ and $x$ in quadrant IV.
1
vote
4answers
70 views
Are these trigonometric “statements” equal
In my Calculus book I have one statement:
$$\cos(2x) = \cos^2(x)-\sin^2(x)$$
and a couple of rows down another statement is:
$$ \cos(2x) = 2 \cos^2(x) - 1 = 1 - 2 \sin^2(x).$$
Now when trying to ...
