Solving Trigonometry Equations and Problems with Examples and Tips

Solve trigonometric equation $\sin 14 x - \sin 12 x + 8 \sin x - \cos 13 x = 4$

tibukooinm 2022-03-22

Solve this problem:
$lim_{x \to \frac{π}{2}} \frac{\cot x}{2 x - π}$

Deegan Chase 2022-03-22

Solve the following question:
$9 \sin 2 x - 40 \cos 2 x = \frac{41}{\sqrt{2}}$

Lorelei Stanton 2022-03-22

Solve the equation:
$f (n) = \cot^{2} (\frac{π}{n}) + \cot^{2} (\frac{2 π}{n}) + \dots + \cot^{2} (\frac{(n - 1) π}{n})$
then how to find limit of $\frac{3 f (n)}{(n + 1) (n + 2)}$ as $n \to \infty$ ?

Anika Boyd 2022-03-22

Solve the equation
$\cos \frac{4 x}{3} = \cos x + 1$

nomadzkia0re 2022-03-22

Let $θ = \frac{2 π}{5}$ .
Show $2 \cos (2 θ) + 2 \cos (θ) + 1 = 0$ .

Roy Roth 2022-03-22

Writing $\frac{\sin x + 3 \cos x}{2 \cos x}$ in a form that uses only one trig function ( $\sin, \cos, \tan$ , etc)

Paula Good 2022-03-22

Why $\frac{\sec^{2} x}{\sqrt{\sec^{2} x}} \neq \sec x$ ?
When I evaluate $\frac{d}{d x} ({sinh}^{- 1} (\tan x))$ , i get:
$\frac{\sec^{2} x}{\sqrt{1 + \tan^{2} x}}$
At this point I want to use the $\sec^{2} x = 1 + \tan^{2} x$ identity to simplify to:
$\frac{\sec^{2} x}{\sec x} = \sec x$

Harold Hoover 2022-03-22

Given $2 \sin (α) + 2 \sin (β) = 3 \sin (α + β)$ prove $\tan (\frac{α}{2}) \tan (\frac{β}{2}) = \frac{1}{5}$

blestimd4pz 2022-03-21

Solve the following equation
$3^{x^{2} - 6 x + 11} = 8 + \cos^{2} \frac{π x}{3}$
Here is the problem that I am struggling with it I tried to take a logarithm of both side but I kinda stuck can someone help me with this? Thanks

Zack Mora 2022-03-21

Solve the equation $\sin (3 x) \cos (x) = \frac{2}{3}$ for $x \in [0, \frac{π}{2})$ but I could not do it. I tried to develop $\sin (3 x) = \sin (x + x + x)$ and I arrived at the step where the equation becomes $(4 \cos^{2} (x) - 1) \sin (x) \cos (x) = \frac{2}{3}$ and I could not go further !

Pizzadililehz 2022-03-21

Solve system of equations: $\sqrt{2} \sin x = \sin y, \sqrt{2} \cos x = \sqrt{5} \cos y$
I tried to use tangent half-angle substitution, tried to sum these two equations and get this
$\sin (x + \frac{π}{4}) = \frac{\sqrt{3}}{\sqrt{2}} \sin (y + \tan^{- 1} (\sqrt{5}))$ and i stuck

ezpimpin6988ok1n 2022-03-21

Solve $\tan x \cos 2 x = \frac{1}{5}$ for $0^{\circ} < x < 360^{\circ}$
Can I get some hints for solving this trigonometry equation?

Jaylin Clements 2022-03-21

Main period of $f (x) = \cos 5 x + \cos 10 x$
$f (x) = \cos 5 x + \cos 10 x$
$f (x) = \cos 5 x + 2 \cos^{2} (5 x) - 1$
$f (x) = 2 \cos^{25} x + \cos 5 x - 1$
have tried to further simplify the function to a complete square or a function like $\cos^{2}$ (something) but I was not able to. Then I factorised:
$f (x) = 2 (\cos 5 x + \frac{1}{2}) (\cos 5 x - 1)$
where each multiplier has a period of $\frac{2 π}{5}$ which makes me think that the main period of the function is $\frac{2 π}{5}$ .

London Douglas 2022-03-21

Let $x_{1} and x_{2}$ be the roots of the equation : $x^{2} - 2 \sqrt{2} x + 1 = 0$
Calculate $\arctan (x_{1}) \cdot \arctan (x_{2})$

Aryan Salinas 2022-03-21

Let $A = f^{2} + g^{2}$ , where f,g are functions of x such that
$f^{'} = (c - 1) (f \cos (x) \sin (x) + g \sin^{2} (x))$ ,
$g^{'} = - (c - 1) (f \cos^{2} (x) + g \cos (x) \sin (x))$ ,
for some constant c.
How do I show that $A^{'} \leq 4 | c - 1 | A$ ?

Find the solution of cos B csc B tan = 1

Sinh3tcos2t

Kason Palmer 2022-03-20

Solve trigonometric integral
$\int_{- \frac{π}{2}}^{\frac{π}{2}} \frac{\sin^{2014} x}{\sin^{2014} x + \cos^{2014} x} d x$

Oxinailelpels3t14 2022-03-20

Solve this trigonometric equation ${\tan^{2}} x + {\cot^{2}} x - 3 (\tan x - \cot x) = 0$

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