Solving Trigonometry Equations and Problems with Examples and Tips

Find the value of $\sin (\cos^{- 1} (\frac{1}{2}) + \sin^{- 1} (\frac{3}{5}))$

Yaritza Estrada 2022-04-07

Find the range of A if $A = \sin^{20} x + \cos^{48} x$

Quinn Dean 2022-04-07

I've attempted to integrate the function:
$\frac{2 x + 7}{x^{2} + x + 1}$

Bryson Whitney 2022-04-07

I'm trying to prove the following problem:
$\frac{\sec^{2} (x)}{\cot (x)} - \tan^{3} (x) = \tan (x)$

Devin Dougherty 2022-04-07

I'm stuck on this problem:
If ,
then find the value of:
$2^{n} \prod_{k = 0}^{n - 1} \cos (2^{k} θ)$

Destinee Adams 2022-04-07

I'm trying find an exact value for
$\cos (\frac{1}{3} \arctan (\frac{- 10}{9 \sqrt{3}}))$

fanairana7lu1 2022-04-07

I would like to know why $\frac{\sin (n)}{n^{2}} < \frac{1}{n^{2}}$ ? It becomes obvious when you look at a graph, but for instances where you can’t do that how do you tell if the comparison is true?

Emmy Decker 2022-04-07

I was solving the trigonometric equation
$\tan^{2} x + \cot^{2} x = 2 - \cos^{2014} (2 x)$

Willie Kelley 2022-04-07

I was trying to find two limits which are trivial using l'Hopital, but I can't seem to find a way to do it without it. For example :
$f (x) = \frac{e^{2 \sin (x)} - 1}{x}$
I tried to do it using the fact I know $lim \frac{e^{x} - 1}{x} = 1$ as $x \to 0$ . Then,as $2 \sin x$ tends to 0 as well as $x \to 0$ , I first tried to prove the limit of $f (x)$ would be 1, but I know it is 2 (using l'hôpital).

Leia Sullivan 2022-04-07

I would like to compute
$\int_{0}^{2 π} \frac{\sin^{4} (4 x)}{\sin^{2} (x)} d x$

Blaine Jimenez 2022-04-07

I want to show that $x = \cos \frac{π}{11}$ is a solution of equation :
$8 x^{2} - 4 x + \frac{1}{x} - 4 = 4 \sqrt{\frac{1 - x}{2}}$

Alan Zavala 2022-04-07

I wanted to use this
$\sin (\frac{π}{15}) \cdot \sin (2 \frac{π}{15}) \dots \sin (7 \frac{π}{15}) = \sqrt{15}$

Emilia Hoffman 2022-04-07

I want to evaluate
$\int \frac{\cos θ d θ}{\sqrt{2 - 9 \sin^{2} θ}}$

Aliyah Mendez 2022-04-07

I want to know if it's true.
$\sin (\frac{π}{2} + 2 π K) > \sin (3 (\frac{π}{2} + 2 π k))$

Lisa Cooper 2022-04-07

I need to write this functions in rectangular coordinates:
$f (r, θ) = r^{2 k + 5} \cos 5 θ$
$g (r, θ) = r^{2 k + 5} \cos 5 θ$

Keenan Rhodes 2022-04-07

How to simplify the trigonometric term?
$\frac{2 \tan (\frac{x}{2})}{{(\tan (\frac{x}{2}) - 1)}^{2}} + \frac{\tan^{2} (\frac{x}{2}) + 1}{2 \tan (\frac{x}{2})}$

Bryanna Leon 2022-04-07

I need to 'prove' that
${(1 + \cot (x))}^{2} - 2 \cot (x) = \frac{1}{(1 - \cos (x)) (1 + \cos (x))}$

Colt Rhodes 2022-04-07

I need to isolate y. I've been trying to change the $\tan$ for the $\cos$ but at the end I don't know how to continue.
$x = \tan (3 y) + \frac{1}{\cos (3 y)}$

Marshall Wolf 2022-04-07

How to Simplify
$- \frac{1}{4} \sin \frac{x}{4} + \frac{\sqrt{3}}{4} \cos \frac{x}{4} = 0$

Lilliana Villa 2022-04-07

How to show $\tan \frac{π}{7} < \sin \frac{5 π}{18}$ without a calculator?
Attempts:Since both sides are greater then zero, we can compare the squares of the functions.Replaced $\tan \frac{π}{7}$ with $\cot (\frac{π}{2} - \frac{π}{7}) = \cot \frac{5 π}{14}$ . Then I replaced ${(\sin \frac{5 π}{18})}^{2}$ with ${(\frac{1}{1 + \cot \frac{5 π}{18}})}^{2}$ . Then I tried to simplify the difference, but it didn't clarify anyhing. Could you please help me compare those functions?

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