Solving Trigonometry Equations and Problems with Examples and Tips

Simplifying $\frac{\sum_{i = 1}^{i = n} 1 + \tan^{2} θ_{i}}{\sum_{i = 1}^{i = n} 1 + \cot^{2} θ_{i}}$ , where $θ_{i} = \frac{2^{i - 1} π}{2^{n} + 1}$

Courtney Griffin 2022-01-25

In any triangle is $\sin A + \sin B + \sin C = \frac{3 \sqrt{3}}{2}$ always Well, I came with an interesting proof. But I just want to verify it Applied at function $y = \sin x$ We have, $\sin (\frac{A + B + C}{2}) \geq \frac{\sin A + \sin B + \sin C}{3}$ From here we will get $\sin A + \sin B + \sin C \leq \frac{3 \sqrt{3}}{2}$ Also by A.M. $\geq$ G.M. in an acute angled triangle $\frac{\sin A + \sin B + \sin C}{3} \geq \sqrt[3]{\sin A \sin B \sin C}$ $\Rightarrow \sin A + \sin B + \sin C \geq 3 (\sqrt[3]{\sin A \sin B \sin C})$ $\Rightarrow \sin A + \sin B + \sin C \geq 3 (\frac{\sqrt{3}}{2}) = \frac{3 \sqrt{3}}{2} > 2$ and from this I get $\sin A + \sin B + \sin C \geq \frac{3 \sqrt{3}}{2}$

Laney Spears 2022-01-25

Adding two cosine waves, result in the standard $A \cdot \cos (ω t + B)$ form
$y (t) = \cos (40 t) - 0.3 \cos (40 t - 16)$
This combines two waves of the same frequency but different phases, and the objective here is to add them and present the result in the simplified form, as a single real amplitude multiplied by a single cosine. I have tried complex analysis, via $R e [e^{i 40 t} (1 - 0.3 e^{- i 16})]$ , but I still can't get a result out of it.

logosomatw 2022-01-25

Find the least value of $\sec^{6} x + \csc^{6} x + \sec^{6} x \csc^{6} x$

Seamus Kent 2022-01-24

value of $2 \tan^{- 1} (\csc α) + \tan^{- 1} (2 \sin α \sec^{2} α)$

Seamus Kent 2022-01-24

Proving $\frac{1 + \csc^{2} A \tan^{2} C}{1 + \csc^{2} B \tan^{2} C} = \frac{1 + \cot^{2} A \sin^{2} C}{1 + \cot^{2} B \sin^{2} C}$

treetopssan 2022-01-24

Prove angle addition holds for $R^{n}$
Define $θ (u, v) = \cos^{- 1} (\frac{u \cdot v}{| u | | v |})$ be the angle between $u, v \in R^{n}$ , where $u \cdot v$ is the standard inner product and $| x | = \sqrt{x \cdot x}$ for all $x \in R^{n}$ . Let w=su+tv where $s, t \geq 0$ are scalars. Show $θ (u, v) = θ (u, w) + θ (v, w)$ for $u, v \neq 0$

Vilharjevw7 2022-01-24

Simplifying $\sin^{2} (α) \cos^{2} (α)$

framtalshg 2022-01-24

Elementary proof of Bhaskara Is

Jamya Elliott 2022-01-24

How to solve $\cos (\sin^{- 1} (- \frac{3}{5}))$ ?
I tried solving it using the formula $\sin^{2} x + \cos^{2} x = 1$ and I also got $\frac{45}{}$ as the answer but I got it by inputting the value of cosx in the given question in place of
$\sin^{- 1} (- \frac{3}{5})$
But I cant see any logic there.

Shamar Padilla 2022-01-24

How $\cos^{2} (2 x))^{2} = \frac{1}{4} {(1 + \cos (4 x))}^{2}$
Can you please give me the proof for $\cos^{2} (2 x))^{2} = {\frac{14}{1 + \cos (4 x)}}^{2}$
I know that $\frac{12}{\cos (2 x) + 1} = \cos^{2} x$

joygielymmeloiy 2022-01-24

Proving $\frac{\cot θ - \csc θ + 1}{\cot θ + \csc θ - 1} = \csc θ - \cot θ$

jelentetvq 2022-01-24

Using the general solution for solve $\sin x = \sin y$
We know that $\sin x = \sin y$ implies that $x = 2 k π + y or x = 2 k π + π - y$ . If we want to solve $\sin x = \sin x$ using this method, it gives $x = 2 k π + x or x = 2 k π + π - x$ but it's obvious that solution is $x \in R$ . Why this happens? There is a similar problem for cosx=cosx.

tripplek7i 2022-01-24

Double angle formula equation $\sin (2 x) \cos (2 x) = \frac{1}{4}$

treetopssan 2022-01-24

If $\sin θ - \cos θ \leq μ (\cos θ + \sin θ)$ , then $\tan θ \leq \frac{1 + μ}{1 - μ}$

Carly Shannon 2022-01-24

Why is this true? $\int \frac{d u}{\tan u \cos^{2} u} = \int \frac{d (\tan u)}{\tan u}$

Jamya Elliott 2022-01-24

Solve $\tan x = {\sec 42}^{\circ} + \sqrt{3}$

Natasha Henry 2022-01-24

Given $lim_{x \to 0} \frac{\sin (x)}{x} = 1$ , Prove $lim_{x \to 0} \frac{\sin (x)}{\sin (m x)} = \frac{1}{m}$ for m>0

Anika Osborne 2022-01-24

Prove that $\tan \frac{π}{9} + 4 \sin \frac{π}{9} = \sqrt{3}$

joygielymmeloiy 2022-01-24

Solving $2 \sin (x + 30^{\circ}) = \cos (x + 150^{\circ})$ for x between $0^{\circ} and 360^{\circ}$

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