Solving Trigonometry Equations and Problems with Examples and Tips

Isolating y in $\sin (x y) = \cos (x y)$
Given $\sin (x y) = \cos (x y)$ , what is the best way to isolate y? Since $\sin (\frac{π}{2}) = \cos (\frac{π}{2})$ it would seem intuitive to say that $x y = \frac{π}{2}$ and thus that $y = \frac{π}{2 x}$

dikcijom2k 2022-07-13

How to solve $\frac{3}{2} x - \frac{4}{5} = \sqrt{\sin (30^{\circ}) + \sin \frac{7 π}{4}}$

fythynwyrk0 2022-07-13

Solve $\frac{2}{\sin x \cos x} = 1 + 3 \tan x$

Ximena Skinner 2022-07-13

Proving that $\frac{\sin α + \sin β}{\cos α + \cos β} = \tan (\frac{α + β}{2})$

auto23652im 2022-07-13

If $\tan^{2} (θ) + 2 \sec^{2} (θ) = 5$ . Find the value of $\sin^{2} (θ)$

pablos28spainzd 2022-07-13

how to evaluate $\tan x - \cot x = 2$

Blericker74 2022-07-13

how to find $\tan (\frac{x}{2})$ knowing that $\cos (x) + \sin (x) = \frac{7}{5}$

Jovany Clayton 2022-07-13

What is $\tan^{- 1} (5 i / 3)$
My progress: Let $\tan x = \frac{5 i}{3} = \frac{\sin x}{\cos x}$ I tried using $\sin x = \frac{e^{i x} - e^{- i x}}{2}, \cos x = \frac{e^{i x} + e^{- i x}}{2}$ to show that $\frac{e^{i x} - e^{- i x}}{e^{i x} + e^{- i x}} = \frac{- 5}{3}$ or $e^{2 i x} = \frac{- 1}{4}$ , but I'm stuck here.

Desirae Washington 2022-07-13

How do I evaluate the limit
$lim_{x \to 0} ⌊ \frac{\tan x \sin x}{x^{2}} ⌋$

gaiaecologicaq2 2022-07-13

Solve $\tan 2 x = 1 / \sqrt{3}$ for $- 180 \leq x \leq 180$

ban1ka1u 2022-07-12

Here is the expression:
$2 (\sin^{6} x + \cos^{6} x) - 3 (\sin^{4} x + \cos^{4} x) + 1$

DIAMMIBENVERMk1 2022-07-12

$\tan (x + y i) = α + β i \Rightarrow \tan (x - y i) = α - β i$ ?

Jaydan Aguirre 2022-07-12

Given $\tan β = \frac{n \sin α \cos α}{1 - n \sin^{2} α}$ , show that $\tan (α - β) = (1 - n) \tan α$

Maliyah Robles 2022-07-11

General solution to $(\sqrt{3} - 1) \cos x + (\sqrt{3} + 1) \sin x = 2$

vasorasy8 2022-07-11

Solve for the positive values of x in $\ln (e^{\frac{1}{2}} + \sin x) = \frac{1}{2}$

ScommaMaruj 2022-07-10

Solve the following equation for $- 180^{\circ} \leq x \leq 180^{\circ}$
$\sin 2 x = \tan x .$
I am aware that I can convert $\sin 2 x = 2 \sin x \cos x$ . However, I am not sure where to go from here to find the values for x that will make the equation hold. Any help with solving this would be very much appreciated.

Ciara Mcdaniel 2022-07-10

I would like to show that $\sin^{- 1}$ is an increasing function. In other words, I want to show that
$x_{1} \leq x_{2} \to \sin^{- 1} (x_{1}) \leq \sin^{- 1} (x_{2}) .$
I fail to see how to start this. Also, if possible, I would like to show this without using other functions (e.g. sin) known to be increasing/decreasing.

Wisniewool 2022-07-10

find the maximum of the function $f (x) = a + b \sqrt{2} \sin x + c \sin 2 x, 0 < x < \frac{π}{2}$

Bruno Pittman 2022-07-10

If
$\begin{matrix} (1) & \sin y + \cos y = \frac{1}{2} \end{matrix}$
Then find
$\begin{matrix} (2) & x = \frac{\sin^{3} y}{\cos^{2} y} + \frac{\cos^{3} y}{\sin^{2} y} \end{matrix}$

Gauge Terrell 2022-07-10

Compute $\int_{0}^{π / 2} \frac{\cos x}{2 - \sin 2 x} d x$

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