Solving Trigonometry Equations and Problems with Examples and Tips

When is $\sin^{3} (x) > \cos^{3} (x)$ ?

Marzadri9lyy 2022-03-24

General formulas for $\cos (\sum_{i = 1}^{n} θ_{i})$ and $\sin (\sum_{i = 1}^{n} θ_{i})$

parksinta8rkv 2022-03-23

Solve this equation.
${(\sqrt{\sqrt{2} + 1})}^{\sin (x)} + {(\sqrt{\sqrt{2} - 1})}^{\sin (x)} = 2$

Coradossi7xod 2022-03-23

Solve this trigonometric inequality:
$\sin x \sin 2 x - \cos x \cos 2 x > \sin 6 x$

annlanw09y 2022-03-23

Solve the following integral:
$\int_{0}^{4 π} \frac{x | \sin x | d x}{1 + | \cos x |}$

Oliver Tyler 2022-03-23

Solve the following equation
$2 \arccos (x) - \arcsin (2 x \sqrt{1 - x^{2}}) = 0$

rhedynogh0rp 2022-03-23

Solve the equation
$4 y^{2} - 20 x - 25 = 0$

Amya Horn 2022-03-23

Solve the equation
$\sin (11 x) \sin (x) = \cos (10 x)$

acidizihvzs 2022-03-23

Solve the equation
$27 \sin (x) \cdot \cos^{2} (x) \cdot \tan^{3} (x) \cdot \cot^{4} (x) \cdot \sec^{5} (x) \cdot \csc^{6} (x) = 256$

Deegan Chase 2022-03-23

Solve $x d y - y d x = x \sqrt{x^{2} - y^{2}} d y$

justbethlflql 2022-03-23

Limit of $x^{2} (1 - x \sin \frac{1}{x})$ as $x \to \infty$

Jackson Floyd 2022-03-23

Why can't $\frac{1}{\sin x \cos x}$ be expressed in the form $\frac{A}{\sin x} + \frac{B}{\cos x}$
$\frac{1}{\sin (x) \cos (x)} = \frac{A}{\sin x} + \frac{B}{\cos x} \Rightarrow 1 = A \cos x + B \sin x$
I let $x = \frac{π}{2}$ , getting A=-1. Then I let $x = π$ , getting B=1. This means that $1 = \cos x - \sin x$ which is obviously wrong most of the time.

jisu61hbke 2022-03-23

Why should we have $\sin^{2} (x) = \frac{1 - \cos (2 x)}{2}$ knowing that $\sin^{2} (x) = 1 - \cos^{2} (x)$ ?
Logically, can you not subtract $\cos^{2} (x)$ to the other side from this Pythagorean identity $\sin^{2} (x) + \cos^{2} (x) = 1$ ?
When I look up trig identities, however, it says $\sin^{2} (x) = \frac{1 - \cos (2 x)}{2}$

anadyrskia0g5 2022-03-23

Why solving trigonometry equation for $x y^{'} = y \cos \ln \frac{y}{x}$

talpajocotefnf3 2022-03-23

Writing $\tan^{2} (2 \sec^{- 1} (\frac{x}{3}))$ in algebraic form

Paula Good 2022-03-23

Given $\cot (b) = - 2$ find $\sin (4 b)$ and $\cos (4 b)$
I made $\sin (4 b)$ into a expanded form.
$4 \sin (b) \cos^{3} (b) - 4 \sin^{3} (b) \cos (b)$ And then I made a triangle using $\cot (b) = - 2$ for information.
I got from that triangle that, $\sin (b) = \frac{\sqrt{5}}{5}$ and that $\cos (b) = \frac{- 2 \sqrt{5}}{5}$
And from their I simplified.
But whenever I expand $\cos 4 b$ and plug in I get a bad answer, $\frac{353}{25}$ and I do not know if it is correct or wrong.

Alfredo Holmes 2022-03-23

Given $\tan (2 a) = 2$ and $\frac{3 π}{2} < a < 2 π$ find value of $\tan (a)$

Rex Maxwell 2022-03-23

General form for $\sin (k x)$ in terms of $\sin (x) and \cos (x)$
Identities for $\sin (2 x)$ and $\sin 3 x$ , as well as their cosine counterparts are very common, and can be used to synthesize identities for $\sin 4 x$ and above. Given some integer k, is there an equation to find $\sin (k x)$ in terms of $\sin x$ and $\cos (x)$ ?
For example, if I wanted to find the identity for $\sin (1000 x)$ , what would it be?
Identies used:
$\sin (a + b) = \sin (a) \cos (b) + \sin (b) \cos (a)$
$\cos (a + b) = \cos (a) \cos (b) + \sin (a) \sin (b)$

amonitas3zeb 2022-03-23

Geometric proof of $\frac{{\sin 60}^{\circ}}{{\sin 40}^{\circ}} = 4 {\sin 20}^{\circ} {\sin 80}^{\circ}$

Makayla Stevens 2022-03-23

Given , $y = 8 \sec^{2} x + 18 \cos^{2} x$ find the minimum possible value of y.
$y = \frac{8}{\cos^{2} x} + 18 \cdot \cos^{2} x$ find the minimum possible value of y.

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