Solving Trigonometry Equations and Problems with Examples and Tips

Evaluating $\sin (\arccos \frac{1}{2} + \arccos \frac{7}{25})$

Adolfo Hebert 2022-04-05

Evaluate:
$f (x) = (\cos x - \sin x) (17 \cos x - 7 \sin x)$

Marzadri9lyy 2022-04-05

Evaluate without using a calculator:
$\tan (2 \sin^{- 1} (\frac{\sqrt{5}}{5}))$

Pasegeabe85xy 2022-04-05

Evaluate the definite integral:
$\int_{\frac{π}{8}}^{\frac{π}{4}} (\csc (2 θ) - \cot (2 θ) d θ$

Sage Fry 2022-04-05

Evaluate $lim_{y \to 0} \frac{(x + y) \sec (x + y) - x \sec x}{y}$

nomadzkia0re 2022-04-05

Evaluate
$\int_{- \frac{1}{\sqrt{3}}}^{\frac{1}{\sqrt{3}}} \frac{x^{4}}{1 - x^{4}} \cos^{- 1} \frac{2 x}{1 + x^{2}} d x$

Rex Maxwell 2022-04-05

Evaluate
$A = \int_{- 1}^{+ 1} x^{2} - \frac{2}{x^{2} + 1} d x$

navantegipowh 2022-04-05

Evaluate for any integer, n
$\int_{- \frac{1}{2}}^{\frac{1}{2}} \frac{\sin^{4} (n π x)}{\sin^{2} (π x)}$

Kendall Daniels 2022-04-05

Domain of $g (x) = \frac{\cos^{2} x - \sin^{2} x}{1 - \tan x}$ in $R$ ?
In $R$ what is the domain of the function below?
$g (x) = \frac{\cos^{2} x - \sin^{2} x}{1 - \tan x}$
I added two conditions:
$D_{g} = {x \in R : 1 - \tan x \neq 0 \land x \neq \frac{π}{2} + k π, k \in Z}$
This gives me:
$R {x : x = \frac{π}{4} + k π \land x = \frac{π}{2} + k π, k \in Z}$
The solution is only:
$R {x : x = \frac{π}{4} + k π, k \in Z}$

Sanai Huerta 2022-04-04

Expressing the roots of $y^{5} + 11 y^{4} - 77 y^{3} + 132 y^{2} - 77 y + 11 = 0$ terms of of $ζ_{11}$ ?

burubukuamaw 2022-04-04

Expressing $12 \sin (w t - 10)$ in cosine form.

Dumaen80p3 2022-04-04

Evaluating the integral
$\int_{0}^{\frac{π}{2}} (\cos^{5} x) \sin (7 x) d x$ ?

acidizihvzs 2022-04-04

Evaluate:
$\frac{\cos (90 + θ) + \cot (450 + θ)}{\csc (450 - θ) - \tan (180 + θ)} + \frac{\tan (180 + θ) + \sec (180 - θ)}{\tan (360 - θ) - \sec (- θ)}$

Alexis Alexander 2022-04-04

Evaluating
$lim_{n \to \infty} \frac{n}{2} \sqrt{2 - 2 \cos (\frac{360^{\circ}}{n})}$

jermandcryspza3 2022-04-04

Evaluate the indefinite integral
$\int \sin 2 x \sqrt{\cos 2 x + 1} d x$

Marzadri9lyy 2022-04-04

Evaluate $\int_{- \infty}^{\infty} e^{x / 2} s e c h (x) d x$ without Residue Calculus

Caerswso1pc 2022-04-04

Evaluate
${\tan 20}^{\circ} + {\tan 40}^{\circ} + \sqrt{3} {\tan 20}^{\circ} {\tan 40}^{\circ}$

talpajocotefnf3 2022-04-04

Evaluate
$\sum_{{k = 1}}^{13} \frac{\sin (30^{\circ} k + 45^{\circ})}{\sin (30^{\circ} (k - 1) + 45^{\circ})}$
Put $30^{\circ} = α, 45^{\circ} = β$ . Then
$S = \sum_{{k = 1}}^{13} \frac{\sin (α k + β)}{\sin (α (k - 1) + β)} = \sum_{{k = 1}}^{13} \frac{\sin (α (k - 1) + β + α)}{\sin (α (k - 1) + β)}$
$= \sum_{{k = 1}}^{13} \frac{\sin (α (k - 1) + β) \cos α + \cos (α (k - 1) + β) \sin α}{\sin (α (k - 1) + β)}$
$= \cos α \sum_{{k = 1}}^{13} 1 + \sin α \sum_{{k = 1}}^{13} \cot (α (k - 1) + β)$
$= \frac{\sqrt{3}}{2} \cdot 13 + \frac{1}{2} \sum_{{k = 1}}^{13} \cot (α (k - 1) + β)$
Could some help me to solve it, thanks.

meli199939f 2022-04-04

Dual of the formula for Euclidean triangles
It’s well known that the trigonometric area formula for Euclidean triangles is
$S = \frac{1}{2} a b \sin C$ (1.1)
Is there a such formula for hyperbolic triangles?
Is there a proof for (1.1) by using law of cosines?

Tony Mccarthy 2022-04-03

Express $6 θ$ in terms of $\cos θ$

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