Solving Trigonometry Equations and Problems with Examples and Tips

How to prove it?
$2 \sin x \leq x - \frac{π}{3} + \sqrt{3}$

Casertowm7 2022-02-27

Let $z = e^{i t} + 1$ where $0 \leq t \leq π$ , Find the trigonometric representation of $z^{2} + z + 1$

oskrnavih92j 2022-02-27

How can I show that:
$\prod_{k = 1}^{n} (1 + 2 \cos \frac{2 π \cdot 3^{k}}{3^{n} + 1}) = 1$

Arslan Lyons 2022-02-27

Solve this integral:
$\int_{0}^{π} \frac{3 \cos x + \sqrt{8 + \cos^{2} x}}{\sin x} x d x$

fecundavai3c 2022-02-27

Prove that:
$\sum_{n = 1}^{\infty} \frac{\sin (n θ)}{n} = \frac{π}{2} - \frac{θ}{2}$

leciazyg 2022-02-27

How to find the solution x of $2 {\sin 11}^{\circ} {\sin 71}^{\circ} \sin (x^{\circ} + 30^{\circ}) = {\sin 2013}^{\circ} {\sin 210}^{\circ}$

Casertowm7 2022-02-26

If
$\sum_{i = 1}^{\infty} \tan^{- 1} (\frac{1}{2 i^{2}}) = t$

Nettie Potts 2022-02-26

Easiest way to prove that
$\int_{\frac{π}{6}}^{\frac{π}{2}} {\sin (2 x)}^{3} {\cos (3 x)}^{2} d x = {(\frac{3}{4})}^{4}$

hazardetzt10 2022-02-26

Find:
$lim_{x \to 0} \frac{\frac{\sin x}{x} - \cos x}{2 x (\frac{e^{2 x} - 1}{2 x} - 1)}$

Tayyib Cornish 2022-02-26

How to get $\cot (\frac{θ}{2})$ from $\frac{\sin θ}{1 - \cos θ}$ ?

iristh3virusoo2 2022-02-26

Proving:
$\cos A \cdot \cos 2 A \cdot {\cos 2}^{2} A \cdot {\cos 2}^{3} A \dots {\cos 2}^{n - 1} A = \frac{{\sin 2}^{n} A}{2^{n} \sin A}$

enfocarteu7z 2022-02-26

Find all the possible solutions for the equations.
$\tan θ + \sec θ = 2 \cos θ, 0 \leq θ \leq 2 π$

Bradlee Hooper 2022-02-26

My knowledge of trigonometry is still insufficient to resolve this problem. Any help would be greatly appreciated.
$\tan α + 2 \tan 2 α + 4 \tan 4 α = \cot α - 8 \cot 8 α$

trasbocohf1 2022-02-26

I am stuck with this integral:
$\int \frac{d x}{(3 + \cos^{2} x) \cdot \tan x}$

ennuvolat4gv 2022-02-26

Solve:
$\sqrt{2 - 2 \cos x} + \sqrt{10 - 6 \cos x} = \sqrt{10 - 6 \cos 2 x}$

Tagiuraoob 2022-02-26

Which is the easiest way to evaluate:
$\int_{0}^{\frac{π}{2}} (\sqrt{\tan x} + \sqrt{\cot x})$

Anniyah Povey 2022-02-26

Can someone explain why this is true?
$\int_{0}^{2 π} {(\sin n x - \sin k x)}^{2} d x = 2 π$

Bruce Partridge 2022-02-26

I’ve got to proof that:
$\tan (\frac{A}{2}) = \sqrt{\frac{1 - \cos (A)}{1 + \cos (A)}}$

Zaynah Dunn 2022-02-26

Can this:
$\frac{\cos x}{4 + \sin^{2} x}$
Be re-written using the fact that:
$\cot (t) = \frac{\cos (t)}{\sin (t)} = \frac{1}{\tan (t)}$

Scoopedepalj 2022-02-26

How to solve this trigonometric equation $x = \frac{1}{2} \cos (\frac{2}{3} \sin (\frac{3}{4} x)) + 1$
The iterative solution seems to be 1.417.

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