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

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2
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3answers
46 views

Proving $\cos 36° > \tan 36° $

How do we prove that $\cos 36° > \tan 36° $ ? Please help . Thank you.
0
votes
3answers
27 views

$2 \cos^2 x − 2 \cos x− 1 = 0$ Find the solutions if 0° ≤ x < 360°

Find the solutions of $$2 \cos^2 x − 2 \cos x− 1 = 0$$ for all $0° ≤ x < 360°$. For $0° ≤ x < 360°$, I'm getting $x=111.5°$ and $x=248.5°$. Is this correct? Thanks!
2
votes
2answers
36 views

Is $\sec^{-1}(\sec(\pi/2)) = \pi/2$?

I think it shouldn't be defined as $\pi/2$ is not in the range of the function $\sec^{-1}(x)$ Wolfram confused me by giving the answer as $\pi/2$ : Link But it mentions on another page that $\pi/2$ ...
2
votes
0answers
15 views

unit circle trigonometry where angles is greater than 90

how is possible to have sin of angle greater than 90. if sin is ratio of opposite side and hypotenuse in right angle triangle then triangle with one of the angle greater than 90 can not be right angle ...
1
vote
1answer
16 views

finding the coordinate of a point using a distance and an angle from given point

sorry for the simple question and please replay with simple terms I have two points (A, B) where the A is the center of my plot (xA, yA). I know the distance (AB) ...
3
votes
5answers
130 views

$99$th derivative of $\sin x$

Can someone help me calculate the $99$th derivative of $\sin(x)$? Calculate $f^{(99)}(x) $ for the function $f(x) = \sin(x) $
0
votes
1answer
47 views

Differentiation/ find the derivative

Can anybody please help me with my work? I have to find the differentiate/ find the derivative of these two question: Please HELP!!! $sin^2(cos3x^3)^5 $ $cot^2(x)((x^2)(3cos^3(3x)))^2$
1
vote
1answer
11 views

Trig and Inverse Trig Function Compositions

Sorry if this is a dumb question, but I honestly tried searching and all I could find was obvious stuff like $\sin(\arcsin(x)) = x$ So what is the logic behind simplifying expressions like this, ...
2
votes
1answer
26 views

Please assist me with proving this

Prove that if $a$,$b$ and $c$ are angles in a triangle,then $$ \tan\left(\frac{b-c}{2}\right) = \frac{b-c}{b+c}\cot\left(\frac{a}{2}\right) .$$
0
votes
0answers
18 views

Binomial series for $2^{n-1}\cos^n\vartheta$ and $2^{n-1}(-1)^{\frac{n}{2}}\sin^n\vartheta$

Can somebody confirm for me whether the following series are correct? $$2^{n-1}\cos^n\vartheta=\cos ...
0
votes
1answer
19 views

Calculating accelerometer vector when tilted

I'm trying to develop a 3D position estimation program using an xyz accelerometer. Ignoring the massive error introduced by double integration of the acceleration to get displacement, I have another ...
-1
votes
2answers
30 views

Rearrange solution of differential equation involving SHM

This question involves simple harmonic motion (SHM). I am struggling to work out how to rearrange: $x(t)=A\cos(\omega t)+B\sin(\omega t)$ (Which is the solution of the differential equation ...
0
votes
1answer
41 views

find the period of a trigonometric function

I've found the period of this trigonometric function, $$y=\sin^n(x)+\cos^n(x)$$. when n ($n\neq2$)is odd, the period is $2\pi$, when n is even, the period is $\frac{\pi}{2}$. but how to proof it?
3
votes
1answer
56 views

How $\tan{\frac{A}{2}}\tan{\frac{B}{2}}=\frac{1}{2}$,then find $\angle C$

In $\Delta ABC$, if $$\tan{\dfrac{A}{2}}\tan{\dfrac{B}{2}}=\dfrac{1}{2}\\\sin{\dfrac{A}{2}}\sin{\dfrac{B}{2}}\sin{\dfrac{C}{2}}=\dfrac{1}{10}$$ Find the $\angle C$ My try: since ...
1
vote
1answer
41 views

solve this problem of trigonometry.

It is given : $$\sin(A-B)/\sin B = \sin(A + Y)/\sin (Y)$$ We have to prove $$\cot B - \cot Y = \cot(A + Y) + \cot(A - B).$$ Please help me solving this. I have tried to solve this by analyzing ...
0
votes
2answers
21 views

When I work out the LHS I get cos(x) as my answer, how do I get to the answer on the RHS?

$\frac{\sin \left(2x\right)}{2\sin \left(x\right)}=\cos ^2\left(\frac{x}{2}\right)-\sin ^2\left(\frac{x}{2}\right)$
3
votes
2answers
48 views

Find side length of son-polygon.

Take a regular n sided polygon having side length 1, where n is odd. Draw all diagonals of this polygon. Around the center, you will find a smallest regular polygon similar to bigger one. Tell this ...
0
votes
1answer
26 views

trigonometry question (high school level)

Why does $\cos(50+60) = \cos(115)$? I understand that $\cos(x+y) = \cos(x)\cos(y) - \sin(x)\sin(y)$, but I dont understand how to apply this formula in this question or if I use another method to ...
-1
votes
1answer
18 views

Find tangent from other two trig ratios

I understand the six trig ratios, and know that tangent= opposite/adjacent. I feel like, on a website, I've seen people use either cosine/sine or sine/cosine (can't remember which) to find the ...
0
votes
1answer
12 views

Using Right triangles to determine Values

Missed a day of class, and I can't seem to figure out the concept here. It seems simple but I just can't wrap my head around it. Any and all help is much appreciated.
-1
votes
0answers
19 views

Help solving equation for ramc

I need help solving this equation for RAMC $ASC = ARCCOT (- ( (TAN f x SIN e) + (SIN RAMC x COS e) ) ÷ COS RAMC)$ ASC and RAMC are variables
2
votes
1answer
20 views

Find the value of $(a+b+c)$ when $\cos\theta+\cos^2\theta+\cos^3\theta=1$ and $\sin^6\theta=a+b\sin^2\theta+c\sin^4\theta$

Given: $\cos\theta+\cos^2\theta+\cos^3\theta=1$ and $\sin^6\theta=a+b\sin^2\theta+c\sin^4\theta$ Then find the value of $(a+b+c)$
0
votes
2answers
32 views

Compare the following numbers…

How can I compare this two numbers: $\tan \frac 7{10}$ and $1$? Hope your explanation will be as explicit as possible! Thank you very much!
0
votes
1answer
25 views

Question that includes Trigonometry

In the diagram, $AB = 80 cm$, $\angle ABD = 44^∘$ (Angle B), $\angle BAC = 31^∘$, $\angle DAC =37^∘$ and $\angle DBC = 36^∘$. Calculate: a) $BC$ b) $BD$ c) $CD$
0
votes
0answers
10 views

Angles in 3D space

I am working with a Kinect sensor, in a special case that we are using this I want to calculate the ground position for each of the laser shoots. So basically I have the angle for the shoot that is ...
7
votes
3answers
97 views

Why is $\displaystyle\int^{\infty}_{0}{(1-\cos x)\over{x^{2}}}dx = \frac\pi{2}$?

I have been having trouble understanding Fourier series and analysis in one of my classes. This is one problem from the text and we have to show that this is true. I have done other problems related ...
0
votes
1answer
22 views

Polar graph question

Can you only graph periodic functions using polar graphing? I'm not really understanding this I guess. It you are to get all of the x and y values on a finite graph, then the original must be ...
5
votes
1answer
59 views

Are there any constants other than $\pi$ that give rational or known irrational values for $\cos(\theta)$?

For example: $\cos(\frac{\pi}{3}) = \frac{1}{2}$ $\cos(\frac{\pi}{4}) = \frac{\sqrt{2}}{2}$ Is there any other constant $\theta$ such that $\cos(k\theta)$ is rational or a known irrational where ...
2
votes
1answer
43 views

Explain how the following is equal to $2\cos x$.

The question was Prove $$\frac{1+\sin2x+\cos2x}{\cos x+\sin x}=2\cos x$$ I simplified it using several trigonometric identities, what I got is this "$\dfrac{2\cos^2 x + 2\cos x \sin x}{\cos x + ...
0
votes
2answers
33 views

Trigonometry prove

here the question is that i can prove that the left side=the right side if i use the variable x but if we take (2x=pi on the left side) and (x=pi/2 on the other side) then the equation is not ...
1
vote
2answers
56 views

Is $\sqrt{1-\sin ^2 100^\circ}\cdot \sec 100^\circ = 1$ or $-1$?

The equation will simplify to \begin{align} & = \sqrt{\cos^2 100^\circ}\cdot \sec100^\circ \\[8pt] & = \cos100^\circ\cdot\sec100^\circ \\[8pt] & = 1 \end{align} But the answer key says ...
2
votes
3answers
36 views

Finding tan(A+B)

So I know that $$ \tan(A+B) = \frac{\tan(A) + \tan(B)}{1 - \tan(A) \tan(B)}, $$ but I don`t know how to find $\tan(B)$ for the following problem: If $\tan A = 2/3$ and $\sin B = 5/\sqrt{41}$ and ...
1
vote
3answers
48 views

Area of a Parallelogram

The sides of a parallelogram measure $10$ cm and $18$ cm. One angle of the parallelogram measures $46$ degrees. What is the area of the parallelogram, to the nearest square centimeter? I'm ...
1
vote
1answer
63 views

Expansion of $\sin(a_{1}+a_{2}+…+a_{n})$?

We know this formula: $$\sin(a+b)=\sin a\cdot\cos b+\sin b\cdot\cos a$$ So how to find the of the expansion of this $$\sin(a_{1}+a_{2}+\cdots+a_{n})=\,?$$
1
vote
0answers
18 views

How to approach sketching sine and cosine graphs with transformations

Any tips or suggestions in sketching these graphs quickly, and in ONE go? In exams, I don't want to spend ages re-drawing the original sine/cosine graph, one by one, following each new ...
2
votes
6answers
50 views

General solution for squared trigonometry questions: $\cos^2 x = 1$

$\cos^2 x = 1$ How do you solve trig equations with a power? Unsure what to do with the square? I get this $\frac{1+\cos2x}2 =1$ $\cos2x =1$ $2x=2n\pi\pm0$ $x=n\pi$ but the answer says $\pm ...
1
vote
2answers
27 views

Need help Proving Identities

Prove the Identity: $$\frac{1 + \cos \theta}{\sin \theta} + \frac{\sin \theta}{\cos \theta} = \frac{\cos \theta + 1}{\sin \theta \cos \theta}. $$
1
vote
2answers
27 views

Looking at an angle rotated

Suppose you have an angle of degree theta painted on the ground at a spot. You are standing d distance away and looking at it from a height of h and from your perspective the angle appears to be of ...
0
votes
1answer
42 views

A Question Regarding Trigonometry

For question 7, I have figured out the angles for 2 triangles, the one with RJh and the one with PJh. I don't know what to do after that.
1
vote
3answers
27 views

Find the value of $\sin(B-A)$.

If $A$ is an acute angle whose tangent is $\frac{15}{8}$ and $B$ is and obtuse angle whose sine is $\frac{12}{13}$, find $\sin (B-A)$. [Without calculators] I suppose I gotta use this formula: $\sin ...
0
votes
1answer
45 views

No. of real solutions of the equation $2 \cos (\frac{x^2 + x}{6}) = 2^x + 2^{-x} $

How many real solutions are there of the equation $2 \cos (\frac{x^2 + x}{6}) = 2^x + 2^{-x} $? Please illustrate.
2
votes
2answers
48 views

If $\sin A = \cfrac{3}{5}$ with $A$ in QII, find $\sec2A$.

If $\sin A = \cfrac{3}{5}$ with $A$ in QII, find $\sec2A$. I'm getting $\sec2A=\cfrac{25}{7}$. Is that correct?
4
votes
6answers
111 views

Exact value for $\cos 36°$

Good morning! I'm having trouble with this problem... It's just taking me forever and I'm worn out and I'm lost on how to use a double angle identity for $72=2⋅36$ The problem reads as follows An ...
0
votes
0answers
18 views

What is the Winding Function? [on hold]

I've often heard of a mnemonic device called "SOH-CAH-TOA" used to learn about sine, cosine and tangent. But many of my math peers tell me that this device is not very good because it doesn't give an ...
0
votes
0answers
23 views

combine $\cos2t+\sqrt{\sin2t}$ a single wave of form $A \cos (wt-\theta)$

Combine $\cos2t+\sqrt{\sin(2t)}$ in a single wave of form $$A \cos {(wt-\theta)}$$ Hence plot arough sketch of the graph of the wave
5
votes
2answers
91 views

Solving complex trig functions: $\sin2x + \sin3x = \frac{\sqrt{3}}2$

How to solve: $$\sin(2x) + \sin(3x) = \frac{\sqrt{3}}{2}$$ where $x$ is in $[-\pi,\pi]$? I have no idea what to do with the $\sin(2x) + \sin(3x)$. Am I supposed to factorise, differentiate, is ...
1
vote
1answer
32 views

sum of an arctan series using mathematical induction

How to solve this problem using mathematical induction: $$\arctan (1) + \arctan \Big(\frac13\Big) + ... + \arctan \bigg(\frac{1}{n^2+n+1}\bigg)=\arctan (n+1)$$
0
votes
1answer
16 views

Find term for one angle of two in a trig function

In a right angled triangle, I know that $\tan (x) = \cfrac{4}{z}$ and that $\tan(x+y) = \cfrac{12}{z}$. I need to find an equation which has only $\tan(y)$. The answer is $\cfrac{12}{z} = ...
0
votes
2answers
43 views

If $\sin (B) = − \frac 1 2 $ with $B$ in third quadrant, then find $\cot (B/2)$

If $\sin (B) = − \frac 1 2 $ with $B$ in third quadrant, then find $\cot (B/2)$ I'm getting $-\sqrt{3}-2$
1
vote
1answer
26 views

Would every half angle of an angle in each quadrant be in the previous quadrant?

For example, take (5pi)/4 which is in Q3, it's half angle is (5pi)/8 which is in Q2. Is this true for every angle?