0
votes
2answers
31 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 $-\sqrt{3}-2$
0
votes
1answer
13 views

If $\sin A = 4/5$ with $A$ in QII, find $\cos A/2$

For the following, assume that all the given angles are in simplest form, so that if A is in QIV you may assume that 270° < A < 360°. If $\sin A = 4/5$ with A in QII, find $\cos A/2$ I keep ...
2
votes
1answer
20 views

Prove this identity: $ \tan(2x)-\sec(2x) =\tan(x-\pi/4)$

I've been having a time with this problem. I tried to start with the left side but I hit a dead end quick... I then tried the right side and had a little more luck but I've hit a block. I first used ...
0
votes
2answers
26 views

If $\sin B = −1/2$ with $B$ in QIII, find $\cos B/2$

For the following, assume that all the given angles are in simplest form, so that if A is in QIV you may assume that 270° < A < 360°. If $\sin B = −1/2$ with B in QIII, find $\cos B/2$ Here's ...
1
vote
4answers
38 views

Prove this identity: $\sin^4x = \dfrac{1}{8}(3 - 4\cos2x + \cos4x)$.

The problem reads as follows. Prove this identity: $\sin^4x = \dfrac{1}{8}(3 - 4\cos2x + \cos4x)$. I started with the right side and used double angles identities for $\cos2x$ and a sum and then ...
1
vote
1answer
44 views

Prove $\cos 3\theta = 4 \cos^3\theta − 3 \cos \theta$

$\cos 3θ = 4 \cos^3 θ − 3 \cos θ$ Here's my attempt. Is it correct? Thanks! $\cos(3θ)$ $= \cos(2θ + θ)$ $= \cos(2θ)\cos(θ) - \sin(2θ)\sinθ$ $= (2\cos^2θ - 1)\cosθ - (2\sinθ\cosθ)\sinθ$ $= ...
0
votes
3answers
40 views

Prove this identity? $\cos t ⋅ \cos u ⋅ \cos v = \frac14(\cos(t + u + v)+ \cos(t + u - v)+cos(t-u-v))$

The problem reads as follows. Prove the identity $$\cos t⋅\cos u⋅\cos v =\frac14\big(\!\cos(t + u + v)+\cos(t + u - v)+\cos(t-u-v)\big)$$ Hint: begin with the right side and use cosine sum identity ...
1
vote
3answers
61 views

Range of f(x) = $\frac{\sqrt3\,\sin x}{2 + \cos x}$ [duplicate]

Can you give any idea about the range of the following function? $$f(x) = \frac{\sqrt{3}\,\sin x}{2 + \cos x}$$
2
votes
0answers
32 views

($\cos^4x$)($\sin^2x$) in terms of first power of cosine

I believe that I have his correct but if someone could check it and see that'd be great. Here's a pic! [IMG]http://i58.tinypic.com/2dgm5ic.jpg[/IMG]
0
votes
1answer
30 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 ...
0
votes
2answers
35 views

Was I wrong to omit angles in the solution set for this multiple angle problem?

I may have missed this in my precalculus course, but why was I wrong to omit angles that did not have a positive value for cosine? I didn't include $\frac{3\pi}{4},\frac{7\pi}{12},\frac{5\pi}{4}$ ...
1
vote
1answer
16 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
39 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. ...
0
votes
1answer
24 views

Solve an Angle-Side-Angle special case triangle if it has an obtuse angle?

I've seen this type of problem multiple times on homework, and it's confusing me like mad. The scenario: We have a triangle. It is a special case triangle, with one angle, one side, and another ...
2
votes
2answers
56 views

Trigonometric substitution

Been out of touch with trigonometry for some time now. Need help proving this expression. $$\sin^{2}\left(\frac{x}{2}\right) = \frac{1}{2}(1-\cos\left(x\right))$$ Any help will be appreciated. ...
9
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
2answers
23 views

Solving for x on unit circle equation

I have been given the equation $$\cos^2{x} + 2\sin{x}=2.$$ I have factored it, and the only answer I got was $x=\frac{\pi}{2}$. Is this correct or is there more than one answer? The interval is $0 ...
0
votes
1answer
22 views

Simplifying Trig Identity

I have an equation I have been given to solve, I know how to start but I do not know what to do after I use the Trig Identities. Any help? Here is what I was given $$ \frac{\cos(A + B) + \cos(A - ...
1
vote
1answer
40 views

When is $ 4 ab \sin^2 θ = (a+b)^2 $ ?

I know that by trial and error it is only possible when $ a=b $, but what is the actual solution process?
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: ...
5
votes
2answers
88 views

Show that $\sin 10^\circ$ is irrational

So, this is the problem I am working on. Show that $\sin 10^\circ$ is irrational. The solution to the problem is $$1/2 = \sin 30^\circ = 3 \sin 10^\circ - 4\sin^3 10^\circ .$$ Let $$x = 2\sin ...
0
votes
1answer
43 views

How do I prove this Triginomerty equasion?

I got this in a math preparation course I'm taking for college. Can you please help me proving this? $$\frac{\sin2a\cos a-\cos3a\sin a}{2\sin a}=\cos a$$ Thanks!
1
vote
1answer
131 views

How do I prove this trig identity without geometry?

I need to prove this: $$\cos(x) = \frac{1-\tan^2(\frac{x}{2})}{1+\tan^2(\frac{x}{2})}$$ using only $\sin(a-b)$ and $\cos(a-b)$ formulas wich I already proved. I also proven this: $$\cos^2(x) + ...
0
votes
2answers
88 views

How to prove: $1-\cos 2\alpha = 2\sin^2\alpha$ [closed]

I am taking a preperation course for college. I got this as homework. Prove that: $1-\cos2\alpha = 2\sin^2\alpha$ Thank you!
0
votes
1answer
65 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: $$\sin\left(-\frac{3\pi}{8}\right)=\pm\sqrt{1+\frac{\sqrt2}{2}\over2}$$ ...
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.
1
vote
2answers
24 views

Trig Reduction With Pythagoras #2

If $\sin 10^\circ = p$, then determine $$\sin 280^\circ$$ in terms of $p$. $$\sin 280^\circ=\sin(180^\circ+100^\circ) = -\sin 100^\circ$$ $$-\sin 100^\circ = -\sin(90^\circ+10^\circ) = -\sin ...
1
vote
1answer
19 views

Trig Reduction with Pythagoras

If $\sin 10 = p$, then determine $$\tan^2 30^\circ \times \tan^2190^\circ$$ in terms of p.
1
vote
5answers
67 views

Trigonometric Limits - solution needed

how to solve this problem? (without using l'Hopital rule) $$\lim_{x\to π/2} \frac{1-\sin x+\cos x}{\sin 2x -\cos x}$$ thanks for helping.
1
vote
2answers
28 views

Transforming position function into a sinusoidal function?

Im trying to transform the position function $x(t)=3\sin(\pi t)+4\cos(\pi t)$, into a sinusoidal function of the form $x(t)=A\sin(\omega t+\phi )$. Im trying to follow the steps over at this ...
3
votes
2answers
143 views

Does $\sin(\sin(\sin\cdots(\sin1)\cdots) \rightarrow 0 $?

Stuck on homework problem (not this), if I can prove as a lemma that the sequence $$\sin(\sin(\sin\cdots(\sin1)\cdots) \rightarrow 0 $$ then I'm done. It's monotonic and decreasing and bounded by 0 ...
-1
votes
2answers
26 views

What is the equation for a tangent to the graph of $y=\arcsin(x/2)$ at the origin?

I believe arc sin is the same as inverse sin but then I don't know how to deal with taking the derivative of that.
0
votes
1answer
49 views

A Ferris Wheel Word Problem (Trigonometry)

Please help, will give me an idea how to do more of these. A Ferris Wheel called Colossus has a diameter of 158 feet. Using the figure as a model, find the distance traveled by someone starting at ...
0
votes
0answers
35 views

Stuck with trig substitution

I am stuck with problem at my homework assignment. $$\int \sqrt{1+4x^2}dx$$ I try to apply trigonometric substitution $$x = \frac 1 2\tan{2u}$$ $$dx = \frac 1 {\cos^2{2u}}du$$ But after ...
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 ...
3
votes
3answers
118 views

$\sin^2(x)+\cos^2(x) = 1$ using power series

In an example I had to prove that $\sin^2(x)+\cos^2(x)=1$ which is fairly easy using the unit circle. My teacher then asked me to show the same thing using the following power ...
0
votes
4answers
75 views

Limit: $\lim_{x\to 0} \frac {x-\sin x}{x-\tan x}$

Here's the question: $$\lim_{x\to 0} \frac {x-\sin x}{x-\tan x}$$ I've used l'Hospitals to get $$\lim_{x\to 0} \frac {1-\cos x}{1-\sec^2x}$$ I then tried to use it again, resulting in $= ...
0
votes
2answers
50 views

Find the range of arcsin$((1-x^2)^{0.5})$

Title says it all, how do you get the answer to this? So far I only reach $0<1-x^2<pi/2$ but I get an invalid answer from here. the correct answer is $0<x<pi/2$. Any help is appreciated, ...
0
votes
1answer
43 views

How to solve $\sin^{-1}(\sin\frac{4\pi}{3}) + \cos^{-1}(\cos\frac{4\pi}{3})$?

Ok so this the problem given in my text boo The principal value of $\sin^{-1}(\sin\frac{4\pi}{3}) + \cos^{-1}(\cos\frac{4\pi}{3})$ is (A)$\frac{8\pi}{3}$ (B)$\frac{4\pi}{3}$ ...
1
vote
1answer
38 views

Hairy $u$-substitution problem

Evaluate using the $u$-substitution: $$\int_{-1}^{1} \frac{dx}{4 + x^2}.$$ Now, I was told to set $$\tan u = \frac{x}{2},$$ but that doesn't help me at all. Hints needed!
0
votes
1answer
42 views

Logarithms with trigonometric inequality

My class is going to have an exam tomorrow, but we can't figure out how to solve such equations. $$\log_{\ \large tg(x)} \sqrt{\sin(x)^2 - 5/12} < 1 $$ We tried to transform $1$ to $\log_{\ ...
2
votes
2answers
51 views

How to Prove This Trigonometry Identity?

I have to prove that: $$\tan^2\theta \sin^2\theta = \tan^2\theta - \sin^2 \theta$$ Here is what I have tried $$\tan^2\theta \sin^2\theta$$ ...
1
vote
2answers
73 views

Positivness of the sum of $\frac{\sin(2k-1)x}{2k-1}$.

For $n\in \mathbb{N}$, $x\in (0,\pi)$. Prove that : $$f_n(x)=\sum_{k=1}^n \frac{\sin [(2k-1)x]}{2k-1} \geq 0.$$ I've tried to do it by differentiation : I Calculate $f_n'(x)$ (sum of ...
0
votes
2answers
39 views

Prove that this is an isoceles triangle

I'm trying to solve a problem here. It says: "Prove that a triangle is isoceles if $\large b=2a\sin\left(\frac{\beta}{2}\right)$." $B-\beta$ I've tried to prove it but I can't Can anyone help me?
0
votes
0answers
23 views

Prove that the given triangle is isoceles

I'm trying to solve a problem here. It says: "Prove that a triangle is isoceles if $\large b=2a\sin\left(\frac{B}{2}\right)$." $B-beta$ I've tried to prove it but I can't Can anyone help me?
1
vote
8answers
197 views

Solve $\sin x - \cos x = -1$ for the interval $(0, 2\pi)$

We have an exam in $3$ hours and I need help how to solve such trigonometric equations for intervals. How to solve $$\sin x - \cos x = -1$$ for the interval $(0, 2\pi)$.
1
vote
3answers
39 views

Determining all right-angled triangles with sides $a$, $a+k$ and $a+2k$

Determine all triangles that are right-angled which has the sides: $$a, \quad b = a+k, \quad c = a+2k.$$ (a, k are natural numbers!) So does this mean I have to take a look at: $a^2+b^2=c^2 ...
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: ...
0
votes
4answers
88 views

Help solve a trigonometric equation,

$$3\sin^2(x)+5\sin( x)\cos( x) = 2$$ Can't seem to solve it. Anyone can help me?
0
votes
1answer
57 views

Proof: The coordinates of the witch of Agnesi curve

I need to prove that the coordinates ofthe witch of Agnesi curve is: $$x=2a\cot \theta$$ and $$y=2a\sin ^2 \theta$$ Any idea how to prove it? And I don't understand how we got $a$... (because the ...