0
votes
3answers
28 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!
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 ...
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 ...
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
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?
0
votes
1answer
59 views

Hint finding exact value of half-angle when $\tan (\theta) = {3}$

Unlike others I've tried, I'm having a hard time with this half-angle exercise: If $tan(\theta)={3}$ and $\theta$ is in QIII, find $\tan\left(\frac{\theta}{2}\right)$ Here's what I know (or think I ...
1
vote
1answer
21 views

Check my solution to this trig inequality

Problem $1.88$ : Solve $$\cos x\lt \frac{\sqrt{3}}{2},\qquad x \in [0,2\pi]$$ I found the set of solutions to be $S=[0,2\pi]-\left[\dfrac{\pi}{6},\dfrac{11\pi}{6}\right]$ Is this correct? Thank you.
0
votes
4answers
39 views

Prove that $\sin(\frac{\pi}{3}+x)=\cos(\frac{\pi}{6}-x)$

How to prove that $\sin(\frac{\pi}{3}+x)=\cos(\frac{\pi}{6}-x)$ without using calculus just trigonometry?
1
vote
1answer
19 views

Intersection of graphs, and no solution for trig functions.

All I know is the c=asin(x-b) I don't know how to check the values of b for 'no solutions,' in the case of trig functions. Can someone people provide an algebraic method to solve this.
4
votes
1answer
40 views

Calculate depth using triginometry

I was asked a question like this on an exam today and I'm wondering if I got it right or not. ...
10
votes
10answers
2k views

How to solve $4\sin \theta +3\cos \theta = 5$

Another problem that I already wasted hours on. Given $$4\sinθ +3\cosθ = 5$$ Find $$4\cosθ -3\sinθ$$ Help me guys (PS:I'm not that good in maths)
0
votes
1answer
21 views

Finding the value of trigonometric functions

This is probably one of the easiest concepts but I do not get it, so I am going to give the two problems that are giving me the most trouble on my very long worksheet I have to do, maybe you guys can ...
0
votes
0answers
33 views

Finding the inverse of trig functions

I'm supposed to find the inverse of $$f(x) = \cos(x)+x$$ I usually just substitute $x$ for $y$ and then re-arrange. What do I do in this scenario?
0
votes
2answers
55 views

Is 1 rad important?

Of course radians generally come in ratios of π. So is 1 rad important/useful/special? Or, for that matter, is any integer radian measure important? Besides being approximately 57°, I can't seem to ...
2
votes
1answer
25 views

How do I simplify this difference of angles expression using conjugates?

I'm trying to fill in the gaps in my knowledge of simplifying rational expressions using conjugates, but this one stumps me. Given $\tan(\frac{\pi}{4}-\frac{\pi}{6})$, I can work the formula down to: ...
0
votes
4answers
60 views

How to solve trigonometric equations of the form $\tan(x)=m$ where $m$ is a real number?

How to solve trigonometric equations of the form $\tan(x)=m$ where $m$ is a number? I know how to solve $\sin(x)=m$ where $m$ is a real number and $\cos(x)=m$ where $m$ is a real number but I don't ...
0
votes
1answer
64 views

How to solve $4\sin x\cos x+2\sqrt3\sin x-2\cos x-\sqrt3=0$?

How can I solve the trigonometric equation $$4\sin x\cos x+2\sqrt3\sin x-2\cos x-\sqrt3=0$$ I used to replace $\sin x$ by $\sqrt{1-\cos^2 x}$ but doesn't work very well ;° I just want a hint kiss:°
0
votes
1answer
67 views

How do I simplify a radical within a radical in this half-angle problem?

I don't understand how to simplify the following radicals and arrive at the final answer below. I can make it to this point: $$\sin\left(-\frac{3\pi}{8}\right)=\pm\sqrt{1+\frac{\sqrt2}{2}\over2}$$ ...
1
vote
3answers
36 views

Prove that $\sec^2{\theta}=(4xy)/(x+y)^2$ only when $x=y$

Show that the equation below is only possible when $x=y$ $$ \sec^2{\theta}=\frac{4xy}{(x+y)^2}$$ The only way I can think of doing this is by rewriting it as $$ ...
0
votes
2answers
40 views

Is this a typo, or am I missing something?

I have a handout for my precalc II class. It says $\sinh(-x) = -\sin(x)$ It should be $\sinh(-x) = -\sinh(x)$ right? I don't see how a negative input could make a hyperbolic function circular.
4
votes
2answers
337 views

How can I prove this trigonometric statement true?

$$ {1+\sin^{2}\left(x\right) \over \cos^{2}\left(x\right)} = 1 + 2\tan^{2}\left(x\right)$$ This statement is part of a larger problem, but I need to prove that this is true before moving on. I'm ...
1
vote
2answers
30 views

Sin & Cos Equation/Relation

If sin(x) = 0.3, find cos(pi-x) how i would solve this: let x = sin-1(0.3) solve for cos(pi-[sin-1(0.3)]) Is there a way to solve this by hand? Is the above method wrong?
1
vote
1answer
42 views

Help with this trigonometry problem?

Is there an easier way of doing this problem: A square tower stands upon a horizontal plane. From a point in this place from which three of its upper corners are visible their angular elevations ...
0
votes
2answers
29 views

How can I prove that $2(\cos^6(x)-\sin^6(x))-3(\cos^4(x)+\sin^4(x))=-4\sin^6(x)-1$

How can I prove that $2(\cos^6(x)-\sin^6(x))-3(\cos^4(x)+\sin^4(x))=-4\sin^6(x)-1$ I tried to factor and I got $2\cos^4(x)+(-2\sin^2(x)-3)(\cos^4(x)+\sin^4(x))$ but that doesn't lead me to my goal. ...
1
vote
1answer
42 views

I need to do math from ground up, so what is a good workbook?

Can you guys recommend me a workbook that begins with arithmetic and ends with calculus. Or from pre-algebra to calculus. Like all "Master Math Series" books but in one complete book. It would really ...
1
vote
2answers
72 views

Let $0\,^{\circ}\mathrm{} < A < 45\,^{\circ}\mathrm{}$ . If $420(\tan A + \cot A) = 841$ then find the value of $(116 \cos A − 58 \sin A)$.

Let $0\,^{\circ}\mathrm{} < A < 45\,^{\circ}\mathrm{}$. If $$420(\tan A + \cot A) = 841$$ then find the value of $$(116 \cos A − 58 \sin A)$$ One way to solve this is by usual method , that is ...
0
votes
1answer
30 views

How can I write $\frac{(4k-15)\pi}8$ as $n+2k\pi$ where $k\in\mathbb Z$ and $n\in(-\pi,\pi]$

How can I write $\frac{(4k-15)\pi}8$ as $n+2k\pi$ where $k\in\mathbb Z$ and $n\in(-\pi,\pi]$ $\boxed{\bf My\,try::}$ $$\begin{align} \frac{(4k-15)\pi}{8}&=\frac{4k\pi-15\pi}{8}\\ ...
0
votes
1answer
50 views

Someone can explain me why $\tan(-\frac{\pi}4+\arctan x)=\frac{x-1}{x+1}$

Someone can explain me why $tan(-\frac{\pi}4+\arctan x)=\frac{x-1}{x+1}$?? I try to understand it, bot I don't understand how to came from one side to the other... Thank you!
0
votes
4answers
44 views

$4\cos x^2 - 4\cos x = 2$, find all solutions in the interval $0^º\leq x\leq 360^º$

$4\cos x^2 - 4\cos x = 2$, find all solutions in the interval $0^º\leq x\leq 360^º$ I'm not sure what I'm overlooking or not doing right but I can't seem to figure it out. I've tried factoring ...
2
votes
3answers
114 views

$\cos(x)+\cos(3x)+…\cos(2n-1)x=\sin(2nx)/2\sin(x)$

I need to somehow show that $$\cos(x)+\cos(3x)+...\cos(2n-1)x=\frac{\sin(2nx)}{2\sin(x)}$$ for some integer n>0. This seems impossible to me since if I consider the Left Hand Side, I don't know any ...
3
votes
3answers
90 views

How to write $x=2\cos(3t) y=3\sin(2t)$ in rectangular coordinates?

How would I write the following in terms of $x$ and $y$? I think I use the inverse $\cos$ or $\sin$? $$x=2\cos(3t)\,, \quad y=3\sin(2t)$$
0
votes
1answer
59 views

Solving the equations below : $\cos4x=\cos(x+\pi)$

$\cos 4x = \cos (x+\pi)$. Is the answer : S={60°, 36°} or S={60°,300°} please help and tell me why ? When the cosine in the first quarter and the fourth. .
2
votes
2answers
60 views

How do you find two functions $f$ and $g$ such that $f(x) \cdot g(x)=f(x)-g(x)$?

This was inspired by this question ( Logarithms with trigonometric inequality ) I already know the answer ( $f(x)=\tan^2 x$ and $g(x)=\sin^2 x$). However I am interested in how to find this answer. ...
1
vote
1answer
63 views

DF equation: solve for x

OK, i know what to do with the first and second term. Could someone please help with the third and solve for x? :) [This might seem a silly question though.]
2
votes
0answers
63 views

Bretschneider-Brahmagupta-Heron Proof

Derive Bretschneider's formula, Brahmagupta's formula and Heron's formula in one memorable elegant proof. I ask this question merely to see the creativity of the MSE community when it comes to ...
1
vote
1answer
89 views

How to prove this trigonometric identity?

$$\sum_{k=1}^n\frac{1}{\displaystyle \sin^4\left(\frac{k\pi}{2n+1}\right)}=\frac8{45}n(n+1)(n^2+n+3)$$ I think it maybe use $\cos(nx)+i\sin(nx) = \displaystyle\sum_{k=0}^n\binom ...
0
votes
5answers
58 views

Prove that $\frac{\sin^2 (2\alpha)}{\sin^2 (\alpha)}=4-4\sin^2 (\alpha)$.

$$\frac{\sin^2 (2\alpha)}{\sin^2 (\alpha)}=4-4\sin^2 (\alpha)$$ I have to solve the left hand side to equal the right hand side.
3
votes
1answer
43 views

How do I get an exact value for the trigonometric expression?

I'm trying find an exact value for $$\cos\left(\frac{1}{3}\arctan\left(\frac{-10}{9\sqrt{3}}\right)\right)$$ Evaluating $\cos(\arctan(\frac{-10}{9\sqrt{3}}))$ is straighforward, but I'm having ...
3
votes
4answers
220 views

How do I prove this trigonmetric identity?

I need to prove that the following identity is true: $$ \frac{\cos^2x-\sin^2x}{1-\tan^2x}=\cos^2x $$ This isn't homework; just a practice exercise. But I keep getting stuck! Thanks much.
2
votes
1answer
89 views

Partial fraction decomposition of $\frac{1}{x^{2n}+a^{2n}}$

I came across a formula for the partial fraction decomposition of $ \displaystyle \frac{1}{x^{2n}+a^{2n}}$. It seems correct (at least for $n=1,2$, and $3$). But how is it derived? ...
1
vote
1answer
23 views

factoring trig functions

I'm having an issue with factoring trig functions. For example the following: $$ x^2 \ cos(2x) + 2x \ sin(2x) \\ $$ I thought it was $$ x(x\ cos(2x) + 2 \ sin(2x)) \\ $$ But this is what my books ...
0
votes
2answers
43 views

Meaning of “edge of the building”?

I'm hoping someone can tell me what they mean "edge of the building" in the following word problem: ...
1
vote
4answers
106 views

Approximation to $\sqrt{\cos(\theta)}$?

I have this formula, (it is just the law of cosines angle formula): $$ d = \sqrt{a^2 + b^2 - 2ab \ cos(\theta)} $$ Here is my issue. I am wondering if there is a way to 'extract' the $cos$ term. My ...
1
vote
4answers
56 views

Trigonometry inside a trapezium

I have the following image, and it's asked to find the values of $X$ and $Y$. I've managed to find it using the this idea: Divide the image in two right triangles and let's call the height of the ...
1
vote
1answer
60 views

A trigonometric equation with many cases

I have to solve the equation $4\cos^m(x)+3\sin^n(x)=5 $ where $m$ and $n$ are non-negative integers. So here comes my question: The case $m=n=0$ is trivial. The case $m=n=1$ is easy to solve. We ...
0
votes
1answer
55 views

Trigonometric eq.

The equation $3\sin(x)+4\cos(x)=5$ is well-known. The equation $3\sin^m(x)+4\cos^n(x)=5$ where $m$ and $n$ are non-negative integers is much more interesting.. I would like to see a nice, elementary ...
1
vote
1answer
73 views

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 $\triangle ABC$ ...
0
votes
2answers
67 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 ...
-1
votes
1answer
34 views

Angular displacement of a certain pendulum bob

The angular displacement $\theta$ of a certain pendulum bob in terms of its initial displacement $\theta_0$ is $$\theta=\theta_0 \cos wt\ .$$ If $w=3.00$ (rad/s) and $\theta_0=\pi/30$ rad, draw two ...