Solving Trigonometry Equations and Problems with Examples and Tips

Proof of
$\sum_{n = 1}^{\infty} \frac{1}{n^{3}} \frac{sinh π n \sqrt{2} - \sin π n \sqrt{2}}{cosh π n \sqrt{2} - \cos π n \sqrt{2}} = \frac{π^{3}}{18 \sqrt{2}}$

ruililorNokmncf 2022-03-31

Proof of
$- \ln (2 \sin (\frac{x}{2})) = \sum_{k = 1}^{\infty} \frac{\cos (k x)}{k}$

Lorelei Stanton 2022-03-30

I need help on proving the following:
$\frac{\cos 7 x - \cos x + \sin 3 x}{\sin 7 x + \sin x - \cos 3 x} = - \tan 3 x$

aanvarendbq28 2022-03-30

I have worked an integral and reduced the integral to
$\frac{n π + \sin (\frac{n π}{2}) - \sin (\frac{3 π n}{2})}{2 n π}$

Rex Maxwell 2022-03-30

I have to prove the following result :
$\frac{\tan θ}{1 - \cot θ} + \frac{c o θ}{1 - \tan θ} = 1 + \sec θ \cdot \csc θ$

Tony Mccarthy 2022-03-30

I have the below question and have to find value of x.
$\cos^{- 1} (\frac{x^{2} - 1}{x^{2} + 1}) + \tan^{- 1} (\frac{2 x}{x^{2} - 1}) = \frac{2 π}{3}$

wibawanyacl3q 2022-03-30

I have an example:
$\frac{49}{64} \cos^{2} θ + \cos^{2} θ = 1$
Then what happens next:
$\frac{113}{64} \cos^{2} θ = 1$
Where has the other cosine disappeared to?

avalg10o 2022-03-30

I have a problem with the following integral
$\int_{- \infty}^{\infty} \frac{x \sin x}{x^{4} + 1}$

fsrlaihq55 2022-03-30

I found out that:
$\tan (x) = x + \frac{x^{3}}{3} + \frac{2 x^{5}}{15} + O (x^{7})$
If I wanted to find a value of $\tan (x)$ , how would I use it to find a value for x?

Liseskirlsojh 2022-03-30

I found this interesting result. Show that
$\frac{1 + {\sin 6}^{\circ} + {\cos 12}^{\circ}}{{\cos 6}^{\circ} + {\sin 12}^{\circ}} = \sqrt{3}$

Pasegeabe85xy 2022-03-30

I don't find the right identities for this
$lim_{x \to \frac{π}{4}} (\tan (2 x) \tan (\frac{π}{4} - x))$

rhedynogh0rp 2022-03-30

I am trying to find an easy way to compute the limit as $x \to 0$ of
$f (x) = \frac{\sqrt{1 + \tan (x)} - \sqrt{1 + \sin (x)}}{x^{3}}$

metalskaashw 2022-03-30

I am trying to find a bound for $| \cos (2 n + 1) θ |$ by something of the form $c (n) | \cos θ |$ . I am suspecting that we can bound it by $(2 n + 1) | \cos θ |$ but I'm not sure how to show that this is true

afasiask7xg 2022-03-30

How to sum up these sine functions?
$A = \sin 2 a + \sin 4 a + \dots + \sin 10 a$

wibawanyacl3q 2022-03-30

How to solve this limit:
$lim_{x \to 0} \frac{\tan 6 x}{\sin 2 x}$

Zack Mora 2022-03-30

How to solve this limit:
$lim_{x \to 0} \frac{\tan^{2} (3 x) + \sin (11 x^{2})}{x \sin (5 x)}$

aanvarendbq28 2022-03-30

how to solve the following problem? If $\sum_{i = 1}^{n} {\cos θ}_{i} = n$ then what is the value of $\sum_{i = 1}^{n} {\sin θ}_{i}$

Sanai Huerta 2022-03-30

$\tan (x) = 3$ . Find the value of $\sin (x)$

peggyleuwpodg 2022-03-30

How to solve $lim_{x \to 0^{+}} \frac{\sqrt{\sin x}}{\sin \sqrt{x}}$ without the use of L'Hospital's Rule

juctommaccedo662f 2022-03-30

$\sin (4 x) = - 2 \sin (2 x)$ solutions in $[0, 2 π)$

The majority of Trigonometry Math problems are quite easy to solve when you have the list of answers that help you see the logic and reasoning. Looking at various examples will help you to see how certain questions are related to provided solutions.

Remember that Trigonometry requires patience and analysis. By following your analysis skills, you will help yourself find the answers. If something remains unclear, start with your exploration of examples again and go step-by-step.

Precalculus

Practice Exercises for Trigonometry