Solving Trigonometry Equations and Problems with Examples and Tips

How to prove
$\sum_{n = 1}^{\infty} \frac{\sin n}{n} = \frac{π - 1}{2}$

sweetrainyday8s2 2022-02-28

Find all the solutions of
$\sin^{5} x + \cos^{3} x = 1$

sweetrainyday8s2 2022-02-28

I am stuck with the simple expression
$\frac{\cos^{2} (θ + α)}{1 - \cos^{2} (θ - α)} = const.$
where $θ$ is a variable and $α$ is the number satisfying
$α = \tan^{- 1} (\frac{4}{3})$

Akash Matthews 2022-02-28

What is the range of the function
$\frac{\sqrt{3} \sin x}{2 + \cos x}$

Umaiza Hutton 2022-02-28

How do you prove this?
$\frac{{(1 - 2 \sin^{2} A)}^{2}}{\cos^{4} A - \sin^{4} A} = 2 \cos^{2} A - 1$

Bruce Partridge 2022-02-28

How am I supposed to prove this inequality?
$\tan (1) \leq \sum_{k = 1}^{\infty} \frac{\sin (\frac{1}{k^{2}})}{\cos^{2} (\frac{1}{k + 1})}$

Zaccagliaodi 2022-02-28

Prove that
$\tan^{- 1} \frac{y z}{x r} + \tan^{- 1} \frac{z x}{y r} + \tan^{- 1} \frac{x y}{z r} = \frac{π}{2}$
where $x^{2} + y^{2} + z^{2} = r^{2}$

Cosmo Truong 2022-02-27

Show:
$\int_{\frac{1}{3}}^{\frac{1}{2}} \frac{arctanh (t)}{t} d t = \int_{\ln 2}^{\ln 3} \frac{u}{2 sinh u} d u$

Kris Patton 2022-02-27

Calculate the following sum for integers $n \geq 2$ :
$\sum_{k = 0}^{n - 2} 2^{k} \tan (\frac{π}{2^{n - k}})$

simnelsbl4 2022-02-27

Prove that
$\tan^{- 1} (\frac{x + 1}{1 - x}) = \frac{π}{4} + \tan^{- 1} (x)$

demonlikw4 2022-02-27

I want to show that
$\cos \frac{2 π}{5} + \cos \frac{4 π}{5} = - \frac{1}{2}, \cos (2 \frac{π}{5}) \cos (4 \frac{π}{5}) = - \frac{1}{4}$

Alexandria Dodd 2022-02-27

What is the usual way of proving things like
$\cos (\frac{π}{6}) = \frac{1}{2} ϕ$ ?

Emmanuella Browne 2022-02-27

Solve
$\frac{\cos x}{1 + \sin x} + \frac{1 + \sin x}{\cos x} = 2$

Corbin Walton 2022-02-27

How can one prove:
$\cos (\frac{π}{7}) + \cos (3 \frac{π}{7}) + \cos (5 \frac{π}{7}) = \frac{1}{2}$

Kris Patton 2022-02-27

Show
$4 \cos^{2} \frac{π}{5} - 2 \cos \frac{π}{5} - 1 = 0$

omdw1u 2022-02-27

Simplifying using the Tangent Difference identity:
$\frac{2 n r}{\tan (\frac{(n - 2) π}{2 n}}}$

oskrnavih92j 2022-02-27

I need to prove that:
$1 + \tan x \tan 2 x = \sec 2 x$

Tagiuraoob 2022-02-27

How do I show that:
$\frac{1}{\sin^{2} \frac{π}{14}} + \frac{1}{\sin^{2} \frac{3 π}{14}} + \frac{1}{\sin^{2} \frac{5 π}{14}} = 24$

Sarah-Louise Prince 2022-02-27

How to prove that:
$\tan (3 \frac{π}{11}) + 4 \sin (2 \frac{π}{11}) = \sqrt{11}$

Ingrid Senior 2022-02-27

How to prove that coefficients of Maclaurin series of $\frac{\arccos (1 - 2 x)}{\sqrt{x}}$ decrease as polynomial degree increases?

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