Solving Trigonometry Equations and Problems with Examples and Tips

Prove that $lim_{x \to 0} [\frac{\arcsin x}{x}] = 1$ and $lim_{x \to 0} [\frac{\arctan x}{x}] = 0$ where [] represents the greatest integer function.

Jaylin Clements 2022-03-30

Prove that $\int_{0}^{\frac{π}{2}} \cos^{m} x \sin^{m} x d x = 2^{- m} \int_{0}^{\frac{π}{2}} \cos^{m} x d x$

abitinomaq1 2022-03-30

Prove that $\int_{2017}^{2018} (\arctan (\ln (x)) - \ln (\arctan (x))) d x > 0$

Dexter Odom 2022-03-30

prove that if $1 \leq m \leq n$ then ${(1 + \frac{1}{n})}^{m} < 1 + \frac{m}{n} + {(\frac{m}{n})}^{2}$

Nadia Clayton 2022-03-30

Prove $\sin (α - β) + \sin (α - γ) + \sin (β - γ) = 4 \cos \frac{α - β}{2} \sin \frac{α - γ}{2} \cos \frac{β - γ}{2}$

Alexis Alexander 2022-03-30

Prove $\cot (x) + \cot (\frac{π}{3} + x) + \cot (\frac{2 π}{3} + x) = \frac{3 - 9 \tan^{2} x}{3 \tan x - \tan^{3} x}$

Milton Robertson 2022-03-30

Prove
${\tan 70}^{\circ} - {\tan 50}^{\circ} + {\tan 10}^{\circ} = \sqrt{3}$

Hanzikoval1pa 2022-03-30

Proof that:
$\cos^{2} 10^{\circ} + \cos^{2} 50^{\circ} - {\sin 40}^{\circ} {\sin 80}^{\circ} = \frac{3}{4}$

Nancy Richmond 2022-03-30

Proof of $\sum_{n = - k}^{k} e^{2 π i n x} = \frac{\sin (2 k + 1) π x}{\sin π x}$

r1fa8dy5 2022-03-30

Proof of
$\arctan 2 = \frac{π}{2} - \frac{\arctan 1}{2}$

michiiiiiakqm 2022-03-29

I need help finding the value of
$\cos (\frac{1}{2} \arccos \frac{3}{5})$

Samara Richard 2022-03-29

I have to prove that:
$\tan^{2} θ \sin^{2} θ = \tan^{2} θ - \sin^{2} θ$

ashes86047xhz 2022-03-29

I have to calculate this Integral -
$\int_{0}^{\frac{π}{2}} \frac{\sin^{\frac{7}{2}} x}{\sin^{\frac{7}{2}} x + \cos^{\frac{7}{2}} x} d x$

Blackettyl2j 2022-03-29

I have the following trigonometric identity
$\cos x - \frac{\cos x}{1 - \tan x} = \frac{\sin x \cos x}{\sin x - \cos x}$

Aleah Choi 2022-03-29

I had to solve for x in this equation:
$\sin (2 x) \tan (x) = \sin (2 x)$

markush35q 2022-03-29

I currently try to simplify the following trigonometric expression:
$\arcsin (2 t - 1) + 2 \arctan (\sqrt{\frac{1 - t}{t}})$

monkeyman130yb 2022-03-29

I am trying to simplify
$2 \cos (6 \frac{π}{7}) + 2 \cos (2 \frac{π}{7}) + 2 \cos (4 \frac{π}{7}) + 1$

Pasegeabe85xy 2022-03-29

How to solve the cubic $x^{3} - 3 x + 1 = 0$
This was a multiple choice question with options being
(A) $- \cos \frac{2 π}{9}, \cos \frac{8 π}{9}, \cos \frac{14 π}{9}$
(B) $- 2 \cos \frac{2 π}{9}, 2 \cos \frac{8 π}{9}, 2 \cos \frac{14 π}{9}$
(C) $- \cos \frac{2 π}{11}, \cos \frac{8 π}{11}, \cos \frac{14 π}{11}$
(D) $- 2 \cos \frac{2 π}{11}, 2 \cos \frac{8 π}{11}, 2 \cos \frac{14 π}{11}$
I tried to eliminate options using the sum and product of roots but I can't figure out if
$\cos \frac{2 π}{9} + \cos \frac{8 π}{9} + \cos \frac{14 π}{9} = 0$
or
$\cos \frac{2 π}{11} + \cos \frac{8 π}{11} + \cos \frac{14 π}{11} = 0$

smaakt4ucq 2022-03-29

$2 \sin (x) = \sin (3 x)$ . Solve for x

amantantawq5l 2022-03-29

How to solve $\cot (2 x) = - \frac{7}{6}$ ?
Trying anything at one point, I thought I could rearrange to get $\tan (2 x)$ then apply $\arctan$ and divide by 2 but that doesn't work.
The angle x is supposed to be 69.7 degrees from the solutions I'm working with.

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