Solving Trigonometry Equations and Problems with Examples and Tips

Given
$\sin (10^{100}) + \sin (n) = 0$
find n.

kembdumatxf 2022-03-25

Further simplify $\tan (α + β) - \tan (β)$
but I keep wondering, whether it's possible to further simplify this, into for example only using the $\tan$ once. I tried using the addition theorems for trigonometry, but these just seem to complicate them further.
I already tried something along this:
$r = \tan (α + β) - \tan (β)$
$= \frac{\tan α + \tan β}{1 - \tan α \tan β} - \tan β$
$= \frac{\tan α + \tan β}{1 - \tan α \tan β} - \frac{(1 - \tan α \tan β) (\tan β)}{1 - \tan α \tan β}$
$= \frac{(\tan α + \tan β) - (\tan β - \tan α \tan^{2} β)}{1 - \tan α \tan β}$
$= \frac{\tan α + \tan α \tan^{2} β}{1 - \tan α \tan β}$

Jasmine Todd 2022-03-24

How do I find out the value of p for $\sin p + \cos p = 0$ ?

markush35q 2022-03-24

How can we prove this identity:
$\sum_{n = 1}^{\infty} \arctan \frac{{(- 1)}^{n}}{ϕ^{2 n + 1}} = \sum_{n = 1}^{\infty} \frac{{(- 1)}^{n}}{\sqrt{5}, ϕ^{4 n - 2}, (2 n - 1), F_{2 n - 1}}$
where $F_{n}$ are the Fibonacci numbers, and $ϕ = \frac{1 + \sqrt{5}}{2}$ is the golden ratio?

monkeyman130yb 2022-03-24

How can one tell the period of $\sin (x^{\frac{3}{2}})$ ? Is it ${(2 π)}^{\frac{2}{3}}$ ?

Polchinio3es 2022-03-24

How can I write the
$\cos^{5} (x)$
as a sum of first order terms? I have started noticing that:
$\cos^{5} (x) = \cos^{4} (x) \cos (x)$
and then:
$\cos^{4} (x) = \cos^{2} (x) \cos^{2} (x)$
Finally:
$\cos^{2} (x) = \frac{1}{2} (1 + \cos (2 x))$
But I would like to find an easier formula, like the one for
$\cos^{2} (x)$

ashes86047xhz 2022-03-24

How can I prove $\sqrt{\sin^{2} (x)} \neq \sin (x)$

Beryneingmk39 2022-03-24

How can I find the value of
$\sin^{24} \frac{π}{24} + \cos^{24} \frac{π}{24}$

Tony Mccarthy 2022-03-24

Help with $\int \frac{1 + \sin x}{(1 + 2 \cos x) \sin x} d x$

Oxinailelpels3t14 2022-03-24

Given the following expression
$w = j \cos [\frac{1}{n} \arccos (\frac{j}{e}) + \frac{m π}{n}] = j \cos (z)$

Kiara Haas 2022-03-24

Given that A,B,C be angles in an acute triangle.
If $(5 + 4 \cos A) (5 - 4 \cos B) = 9$ and $(13 - 12 \cos B) (13 - 12 \cos C) = 25$
find $\cos (A + C)$ . I know $A + B + C = 180^{\circ}$ and $\cos B = - \cos (A + C)$ and what next?

Pablo Dennis 2022-03-24

Given that ${\cos 160}^{\circ} = - q$ , express ${\cos 70}^{\circ}$ in terms of q.

nomadzkia0re 2022-03-24

Given $x = \frac{2 π}{1999}$
Find the value of
$\cos x \cos 2 x \cos 3 x \dots \cos 999 x$

Polchinio3es 2022-03-24

Formula for $\sin {\frac{θ}{3}}$
Using $\sin {3 θ} = 3 \sin {θ} - 4 \sin^{3} {θ}$ ,we may calculate $\sin {\frac{θ}{3}}$
But the formula for root of a cubic equation is very complicated can you help me to find a formula for $\sin {\frac{θ}{3}}$ as it will help to compute ${\sin 20}^{\circ}, {\sin 10}^{\circ}$ etc. which will be useful.

Kendall Daniels 2022-03-24

Let x and y be real numbers such that $\frac{\sin x}{\sin y} = 3$ and $\frac{\cos x}{\cos y} = \frac{1}{2}$ . The value of $\frac{\sin 2 x}{\sin 2 y} + \frac{\cos 2 x}{\cos 2 y}$ can be expressed in the form $\frac{p}{q}$ , where p and q are relatively ' positive integers. Find p+q.

jisu61hbke 2022-03-24

Let $f (x) = \frac{1}{x^{2}} - \frac{1}{\sin^{2} x}$ . Find Value of $lim_{x \to 0} f (x)$ . I've tried L'Hôpital's rule but it didn't work . Also I was unable to use trigonometric identities.

siliciooy0j 2022-03-24

Let $A = {(2 \sin \frac{7 π}{18} + 1)}^{2556}$
How can one find the remainder from the division of [A] by 17?

Oliver Carson 2022-03-24

Let n be a natural number, the Show that
${(\cos (2) + i \sin (2) + 1)}^{n} = 2^{n} \cos^{n} (1) (\cos (n) + i \sin (n))$

parksinta8rkv 2022-03-24

What will be the minimum value of this trigonometric function?
$5 \sin^{2} x - 12 \sin x \cos x + 10 \cos^{2} x$
My doubt is that as this can be written as ${(2 \sin x - 3 \cos x)}^{2} + 1$ and minimum value of $2 \sin x - 3 \cos x$ is -13, so will the minimum value be 14, same as maximum value?

Asher Olsen 2022-03-24

What is the simplest way to compute : $\int_{0}^{π} {(\frac{\sin (x)}{5 - 4 \cos (x)})}^{2} d x = \frac{π}{24}$

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