Solving Trigonometry Equations and Problems with Examples and Tips

Solving for $α$
$\tan α + 2 \tan 2 α + 4 \tan 4 α + 8 \tan 8 α + 16 \tan α = \cot α$

Zack Mora 2022-03-31

$\sum_{k = 1}^{10} (\sin \frac{2 π k}{11} - i \cos \frac{2 π k}{11}) =$ ?

ropowiec2gkc 2022-03-31

$\sin (\frac{x}{2}) + \cos (x) = 0$ , Solve for x of $0^{\circ} \leq x < 360^{\circ}$

Hanzikoval1pa 2022-03-31

How to solve : $\arcsin x - \arcsin (\frac{x}{2}) = \arcsin (\frac{x \sqrt{3}}{2})$
Why can't I figure this one out?? Is it possible to cancel out the arcsins? I know from graphing on my calculator that the answers are -1,0, and 1, but want help getting there by hand.

Polchinio3es 2022-03-31

$\int_{x}^{1} \frac{d t}{1 + t^{2}} = \int_{1}^{\frac{1}{x}} \frac{d t}{1 + t^{2}}$
I showed that
$\int_{x}^{1} \frac{d t}{1 + t^{2}} - \int_{1}^{\frac{1}{x}} \frac{d t}{1 + t^{2}} = \frac{π}{4} - \arctan (x) - [\arctan (\frac{1}{x}) - \frac{π}{4}]$
Since $\arctan (x) + \arctan (\frac{1}{x}) = \frac{π}{2}$ , then it follows that $\int_{x}^{1} \frac{d t}{1 + t^{2}} - \int_{1}^{\frac{1}{x}} \frac{d t}{1 + t^{2}} = 0$ . However, I feel this is kind of proof only "shows" but doesn't really "explains".
Is there another way to prove this? The simpler the better!

Lucian Ayers 2022-03-31

How to solve
$\sec^{2} x + 3 \csc^{2} x = 8$

Nathen Peterson 2022-03-31

How to solve
$\frac{2 \tan x}{1 - {(\tan x)}^{2}} = {(\sin 2 x)}^{2}$

mwombenizhjb 2022-03-31

How to solve
$\frac{1}{\sin x} + \frac{\sqrt{3}}{\cos x} = 4$

jisu61hbke 2022-03-31

$\frac{1}{{\sin 8}^{\circ}} + \frac{1}{{\sin 16}^{\circ}} + \dots + \frac{1}{{\sin 4090}^{\circ}} + \frac{1}{{\sin 8192}^{\circ}} = \frac{1}{\sin α}$ , find $α$

Nathen Peterson 2022-03-31

$\cot^{2} \frac{π}{2 m + 1} + \cot^{2} \frac{2 π}{2 m + 1} + \dots + \cot^{2} \frac{m π}{2 m + 1} = \frac{m (2 m - 1)}{3}$
m is a positive integer.

burubukuamaw 2022-03-31

Proving the identity:
$\sin 3 x + \sin x = 2 \sin 2 x \cos x$

Jazmyn Holden 2022-03-31

Prove:
$\frac{1 - \cos 2 θ}{1 - \cos θ} = 2 \cos θ - 2$

afasiask7xg 2022-03-31

Prove, that
$\sin x - a^{3} \cos x \leq \frac{1}{3} \sqrt{1 + a^{6}}$

Pablo Dennis 2022-03-31

Prove this
$\sin (495^{\circ}) - \sin (795^{\circ}) + \sin (1095^{\circ}) = 0$

Nathanael Hansen 2022-03-31

Prove the trigonometric identity:
$\frac{(\cos^{3} x - \sin^{3} x)}{(\cos x - \sin x)} = \frac{(2 + \sin 2 x)}{2}$

Deegan Chase 2022-03-31

Prove the Identity - Double Angle
$\cot (A) = \frac{\sin (2 A)}{1 - \cos (2 A)}$

xxgetthisar08 2022-03-31

Prove the following
$\sin^{4} x + \cos^{15} x = 1$

blestimd4pz 2022-03-31

Prove the equality
$\tan (π + \frac{x}{3}) > 0$

Rex Maxwell 2022-03-31

Say I want to solve this
$α = 2 \tan^{- 1} (\sqrt{3 - 2 \sqrt{2}})$

Hanzikoval1pa 2022-03-31

Prove that there exists only one number $x \in R$ such that $\sin (x) = x - 1$

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