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

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4
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1answer
68 views

How to find the height of a tower given the distance, angle of elevation, and angle of depression? [on hold]

A building is 16m from a television tower from the top of the building, the angle of depression from the base 43 degrees, and the angle of elevation to the top of the tower is 24 degrees. Find the ...
0
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1answer
32 views

Trigonometry Question - Tough one [on hold]

If in triangle ABC, sin A sin B sin C + cos A cos B = 1. Then find the value of sin C.
0
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3answers
42 views

How to memorize the trigonometric identities?

I am stuck trying to memorize the trig identities, and try as I may, I just can't get them to stick (especially the sum-product and product-sum formulas). I am concerned I won't be able to memorize ...
3
votes
2answers
34 views

Trigonometry Question: find Value of…

Find value of $3 + \cos2x + \cos4x + \cos6x - 4\cos x\cos2x\cos3x$. I tried with $\cos A + \cos B$ identity but it was not simplifying.... Help..
0
votes
3answers
60 views

please help me. ive been trying to solve this for hours [on hold]

At 3:00 PM, a boat is 12.5 miles due west of a radar station and traveling at 11 mph in a direction that is 57.3 degrees south of an east-west line. At what time will the boat be closest to the radar ...
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4answers
53 views

Trigonometric functions of the acute angle

Find the other five trigonometric functions of the acute angle A, given that: \begin{align} &\text{a)}\ \ \sec A = 2 \\[15pt] &\text{b)}\ \ \cos A = \frac{m^2 - n^2}{m^2 + n^2} \end{align} ...
0
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1answer
26 views

Acute angle and trigonometric functions

Given that $\theta$ is an acute angle and $\cos\theta = \dfrac{7}{25}$. Find: $\tan\theta$, $\sin\theta$, $\sec\theta$.
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0answers
26 views

The roots of transcendent equation $\tan(x)=x$ [duplicate]

Can we find the roots of equation $\tan(x)=x$. I once found a formula which gives its roots approximately. Any link will be wlecomed.
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votes
2answers
25 views

Course And Bearing Word problem. [on hold]

**A plane flew 150 miles on a course of 220 degrees and then 130 miles on a course 130 degrees. Then the plane returned to its starting point via the shortest route possible. Find that shortest ...
3
votes
2answers
52 views

Calculation for the chance of finding something a given distance from a starting point by walking straight in a random direction?

The premise is basically a 2D plane with a single point, the starting point. Now a landmark sought by a hiker is a certain distance from that point. If the hiker can only see 1 mile in any ...
2
votes
1answer
42 views

Trigonometric Substitution and the Triangle Inequality

I was reading the solution to this problem: If $x, y, z$ are real numbers and $x+y+z=xyz$ then $x(1 − y^2 )(1 − z^2 ) + y(1 − z^2 )(1 − x^2 ) + z(1 − x^2 )(1 − y^2 ) = 4xyz$ The solution is to ...
6
votes
4answers
716 views

Double Angle Equations

$\cos2x=\frac1{\sqrt2}$ is the original problem, and I have to solve for $x$. However, I'm not sure what to do after I substitute the double angle formulas for $\cos2x$. I know that $\frac1{\sqrt2}$ ...
0
votes
1answer
34 views

Proving the following proportion

$$\frac{a\sin(B-C)}{b^2-c^2}=\frac{b\sin(C-A)}{c^2-a^2}=\frac{c\sin(A-B)}{a^2-b^2}$$ I tried using various things such as sine rule and then replacing the various rations in terms of sides if ...
0
votes
2answers
26 views

Sides and angles of a triangle

$$a \cdot \sin (B-C) +b \cdot \sin(C-A) +c \cdot \sin(A-B) =0$$ where $a, b, c$ are the sides of a triangle and $A, B, C$ are the angles of a triangle No idea how to solve this problem
0
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0answers
28 views

Expand trigonometric expression

I am supposed to expand this expression $${\frac {\sin \left( x \right) b \left( 4\,b\cos \left( x \right) + \sqrt {16\,{b}^{2}+1}+5 \right) }{4\,b\cos \left( x \right) +\sqrt {16 \,{b}^{2}+1}+1}} $$ ...
0
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1answer
15 views

Find points of triangle, one point, all sides and all angles known

Imagine the setup above; how can I calculate the points P1 and P2 if all angles, all sides A,B,C and point P3 are known?
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votes
3answers
63 views

What is the value of $ \int_{x}^{1} \arcsin \left( \frac{2t}{t^2+1} \right) \text{d}t $?

Is this result true? Wolfram doesn't seem to be able to evaluate the definite integral in the allowed time. $$ \int_{x}^{1} \arcsin \left( \dfrac{2t}{t^2+1} \right) \text{d}t = \dfrac{\pi}{2} - ...
1
vote
3answers
56 views

Find a basis of $A = (\{1, \sin(x), (\cos)^2(x), (\sin)^2(x)1\})$ and determining its dimension.

We consider a space F(R,R) of functions of R in R. Let A = ({1, \sin(x), $\cos^2(x)$, $\sin^2(x)$}) Find a basis of the vector subspace of F(R,R) and determine its dimension. So I used the identity ...
0
votes
3answers
37 views

Check my answer for this trigonometric identity

Simplify $\sec x \cot x$ $\sec x = \frac{1}{\cos \theta}$ $\cot x = \frac{1}{\tan \theta}$ therefore $\frac{1}{\cos \theta} · \frac{1}{\tan \theta} = 1(\tan\theta) + 1(\cos\theta) = \frac{\sin ...
0
votes
3answers
109 views

Simplify tan$\theta$ cos$\theta$

How do I simplify tan$\theta$ cos$\theta$ ? Why is this so hard to do? What pieces of information should I know before doing these? Can someone just tell me were am I going wrong? I have 5 days ...
6
votes
2answers
183 views

Integral $\int_{0}^{\pi/2} \arctan \left(2\tan^2 x\right) \mathrm{d}x$

The following integral may seem easy to evaluate ... $$ \int_{0}^{\Large\frac{\pi}{2}} \arctan \left(2 \tan^2 x\right) \mathrm{d}x = \pi \arctan \left( \frac{1}{2} \right). $$ Could you prove ...
1
vote
1answer
36 views

Trigonometric inequality in a triangle

If $\alpha,\beta,\gamma$ are the interior angles in a triangle, the following inequality seems to hold: ...
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3answers
50 views

Simplify $\tan(360 - \theta)$

I am aware that $\tan(\alpha-\beta)=\dfrac{\tan(\alpha)-\tan(\beta)}{1+\tan(\alpha)\tan(\beta)}$ So for my question: $\tan(360 - \theta)$ Do I choose random value for $\theta$ and plug it into the ...
0
votes
3answers
56 views

Simplify $\sin (90 - \theta)$

Title. I have no idea what to do. Is their an identity I have to remember? What am I supposed to do to the equation? Do I have to solve for something first, what does it mean by simplify?
2
votes
2answers
48 views

Different Definitions Of The Sine Function

I was hoping someone could give me a flow chart or high-level map connecting all of the definitions of the sine function, with some of the reasons why we care next to each. I've tried this but I'm not ...
0
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3answers
40 views

Trigonometric Identities help

How do you solve this? I can't figure out what I should do. $$\sin ^4\left(A\right)+\cos ^2\left(A\right)=\cos ^4\left(A\right)+\sin ^2\left(A\right)$$ Also, why is this equal zero? Can someone ...
0
votes
0answers
28 views

Does every triangle have a slope? [on hold]

I have two numbers or two digits to add. One is 0.84 and the other 0.16 both equal to one.If I divide numbers $\frac{1}{0.84}$ and $\frac{1}{0.16}$, subtract one to both results, I would get ...
12
votes
3answers
158 views

How to evaluate $\sum_{n=1}^{38}\sin\left(\frac{n^8\pi}{38}\right)$

Evaluate $$\sum_{n=1}^{38}\sin\left(\frac{n^8\pi}{38}\right)$$ I have found the problem on this page. I have no idea how to do it. Thank you very much.
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2answers
31 views

The bird pointer problem: finding the angle of rotation

Suppose we have a bird pointer. He is a guy that likes to point at birds in the sky: His legs cannot move, however he can rotate around his torso. Also, his body and his arm always make a right ...
2
votes
2answers
76 views

Pick a smart function

Our teacher wants us to find a function $f$ on $(0,\pi)$ such that $$\sqrt{\sin(x)} f(x)^{\frac{1}{4}} =k_1 + \cos(x)$$ and $$\sqrt{\sin(x)} f(x)^{-\frac{1}{4}} = k_2 + \cos(x).$$ The two constants ...
4
votes
1answer
23 views

Family of lines $\sin\alpha x +\sin\beta y +\sin\gamma =0$

Problem : If $\sin(\alpha + \beta)\sin(\alpha -\beta) =\sin\gamma (2\sin\beta +\sin\gamma), 0 < \alpha , \beta ,\gamma <\pi$ then the family of lines $\sin\alpha x +\sin\beta y +\sin\gamma =0$ ...
2
votes
2answers
33 views

How to find the period of the sum of two trigonometric functions

I want to know if there exists a general method to find the period of the sum of two periodic trigonometric function. Example: $$f(x)=\cos(x/3)+\cos(x/4).$$
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0answers
28 views

Trigonometry, find distance of arc movement

Imagine I have the setup as follows: I want to compute the height x in State 2, depending on how much the blue axis have moved. That is, the distance ...
2
votes
1answer
44 views

What trig identities must one know to derive the others?

My TA told me in problem section one day that every trig identity could be derived from just 2: the Pythagorean identity and the double-angle identity (or he might have said the half-angle identity). ...
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0answers
14 views

Steps involved in simplifying trigonometric identities.

I am trying to master the simplification of trigonometric identities. When I look at a problem, asking me to simplify a trigonometric expression, I am not really sure what to do - but I do sort of ...
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votes
2answers
41 views

find a formula for $\sin3 \theta$ in terms of $\sin \theta$,$\cos \theta$ by using an angle-sum formula for sin(2θ+θ) [on hold]

Find a formula for $\sin3 \theta$ in terms of $\sin \theta$,$\cos \theta$ by using an angle-sum formula for $\sin(2 \theta+\theta$)
2
votes
2answers
94 views

How am I supposed to work this out, or do I have to memorize?

When simplifying a trigonometric expression, say, $\sin^2 \theta$ / $\cos^2 \theta$ - I remember that sin over cos is equal to tan. However, what other identities, such as the one mentioned above, ...
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votes
1answer
25 views

Trigonometry - SSS formula to calculate angle of Triangle

I am trying to calculate angle using Law of cosines, SSS formula of Triangle. That is given three sides of triangle, calculate angle between sides. When there is large difference between all sides ...
0
votes
1answer
21 views

Conversion of angle from 360 degree to-90 degree

Here i am trying to convert angle into +90 degree AND -90 DEGREE FORMAT.For desired elevation angle i got answer properly.How to converert angle -90deg to zero, zero to +90 degree format. you can ...
6
votes
7answers
145 views

Value of $\cos^2\alpha-\sin^2\alpha$

My problem is from Israel Gelfand's Trigonometry textbook. Page 48. Exercise 8: b) If $\tan\alpha=r$, write an expression in terms of $r$ that represents the value of $\cos^2\alpha-\sin^2\alpha$. ...
0
votes
1answer
32 views

Integer Solutions to Cosine's Dot Product Formula

Say one wanted to test their students on the dot product formula without a calculator. One would (being a nice teacher and all) natural like to pick numbers in the plane that are "nice" and satisfy a ...
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0answers
32 views

Websites for math tests/quizzes

Next semester I'm taking calculus at college and I was looking for websites that have quizzes/test for things like trigonometry, trig formulas, pre-calculus, calculus readiness, etc. so I can get ...
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2answers
57 views

Trignometric functions, Maximum value

$f(x)=\sin^{16}(x) +\cos^{18}(x)$, find the maximum value of the given function $f(x)$. I tried differentiating the given function however couldn't get the value of $x$ for which I could substitute ...
3
votes
2answers
53 views

Evaluate integral by completing the square and doing trigonometric substitution

$\int \frac{1}{(x-2)\sqrt{x^{2}-4x+3}} dx$ is my problem Complete the square $\int \frac{1}{(x-2)\sqrt{(x-2)^{2}-1}} dx$ I know I'm probably supposed to use $ \frac{d}{dx}\operatorname{arcsec}(u) = ...
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2answers
40 views

How to solve $3 - 2 \cos \theta - 4 \sin \theta - \cos 2\theta + \sin 2\theta = 0$

I have got a bunch of trig equations to solve for tomorrow, and got stuck on this one. Solve for $\theta$: $$3 - 2 \cos \theta - 4 \sin \theta - \cos 2\theta + \sin 2\theta = 0$$ I tried using ...
2
votes
5answers
70 views

Period of $\sin(x) + \cos(x)$

The period of $\sin(x)$ is $2\pi$ and $\cos(x)$ is $2\pi$. And the period of $\sin(x)+\cos(x)$ is also $2\pi$. Why it is so?
3
votes
2answers
54 views

How to find the maximum value of $12\sin x -9\sin^2x$

How to find the maximum value of $12\sin x -9\sin^2x$ ; My approach : This can be written as $-[(3\sin x -2)^2-4]$. It means that the function will be maximum when $(3\sin x-2)^2 <4$ due to ...
2
votes
3answers
138 views

Deriving the sum-to-product identities

I've been asked by my textbook to derive the "sum-to-product" identities from the "product-to-sum" identities. I've attempted to to do this but i've met a dead end, and i'm quite confused. Using ...
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vote
2answers
39 views

Simplify the expression by using a Double-Angle Formula or a Half-Angle Formula.

Simplify the expression by using a Double-Angle Formula or a Half-Angle Formula. (a) $\cos^2 \left( \cfrac{θ}{2} \right)− \sin^2 \left( \cfrac{θ}{2} \right)$ (b) $2 \sin \left( ...
3
votes
1answer
37 views

Range of $f(x)=\frac{\sin x -1}{\sqrt{3-2\cos x-2\sin x}}$ for a specified domain

We are asked to find the range of the function $$f(x)=\frac{\sin x -1}{\sqrt{3-2\cos x-2\sin x}}, \;\;\text{for}\;0\le x\le2\pi$$ I tried to find the range of each basic function of cos and sin then ...