Solving Trigonometry Equations and Problems with Examples and Tips

How to show $\sec^{- 1} (1 + x) = O (x^{\frac{1}{2}})$ as $x \to 0$
According to the definition, I have to find the positive constant C, i.e., I want to obtain:
$lim_{x \to 0} | \frac{\sec^{- 1} (1 + x)}{x^{\frac{1}{2}}} | = C$
Now use the L'hospital's rule:
$lim_{x \to 0} | \frac{\sec^{- 1} (1 + x)}{x^{\frac{1}{2}}} | = lim_{x \to 0} | \frac{\frac{1}{(1 + x) \sqrt{{(1 + x)}^{2} - 1}}}{\frac{1}{2} x^{- \frac{1}{2}}} | = lim_{x \to 0} | \frac{2 x^{\frac{1}{2}}}{(1 + x) \sqrt{{(1 + x)}^{2} - 1}} |$

Aldo Fernandez 2022-04-07

How to prove that $\sin^{4} (x)$ is even
Function is even when f(x)=f(-x), so my aim is to prove that $\sin^{4} (x)$ is even. So I could write it like $\sin^{4} (- x)$ which, in turn, is $(- \sin (x)) \times (- \sin (x)) \times (- \sin (x)) \times (- \sin (x))$ and equal to the one with positive x. Is that enough prove or I should expose it in some other way?

Mary Bates 2022-04-07

How to prove $\frac{1 + \tan x}{1 - \tan x} = \frac{\sec^{2} x + 2 \tan x}{2 - \sec^{2} x}$

Aileen Rogers 2022-04-07

How to proof: $\cos (10^{\circ}) \cdot \cos (30^{\circ}) \cdot \cos (50^{\circ}) \cdot \cos (70^{\circ}) = \frac{3}{16}$

Quinn Moses 2022-04-07

How to integrate this?
$\int \sec^{2} (3 x) e^{\tan (3 x)} d x$

Boston Fitzgerald 2022-04-07

What is the easiest way to solve this trigonometric equation?
$- \sin x - \sin 8 x = \sin 9 x$

daurialebraslmc 2022-04-06

Finding:
$\int_{- \infty}^{\infty} \frac{x^{2}}{x^{4} + 1}$

runddansm88e 2022-04-06

Finding the root mean square of a sum of trig functions
$v (t) = 3 - 2 \sin (t) + 8 \sin^{2} (t)$

George Michael 2022-04-06

Finding sum of $\sum_{{x = 1}}^{17} \frac{1}{1 + \cot^{4} (10^{\circ} x)}$

Sebastian Fox 2022-04-06

Finding $lim_{x \to π} \frac{\sin 5 x}{x - π}$ without using L'Hostpital's rule

Marshall Wolf 2022-04-06

Finding $(\frac{1}{2} + \cos \frac{π}{20}) (\frac{1}{2} + \cos \frac{3 π}{20}) (\frac{1}{2} + \cos \frac{9 π}{20}) (\frac{1}{2} + \cos \frac{27 π}{20})$

Nevaeh Glass 2022-04-06

Finding exact value of trigonometric functions
$\cos (\sin^{- 1} (\frac{12}{13}) + \sin^{- 1} (\frac{4}{5}))$

Nevaeh Glass 2022-04-06

Find traingle ABC satisfies
$1 + 2 \sqrt{2} \sin \frac{B}{2} \sin \frac{C}{2} = \cos B + \cos C$

Reagan Gomez 2022-04-06

Find the y-coordinate given $\cos θ + \sin^{2} θ = - \frac{5}{16}$

Dakota Livingston 2022-04-06

If
$\frac{3 - \tan^{2} \frac{π}{7}}{1 - \tan^{2} \frac{π}{7}} = α \cos \frac{π}{7}$

Alan Zavala 2022-04-06

I'm trying to integrate:
$\int \frac{8 d x}{3 \cos 2 x + 1}$

River Dudley 2022-04-06

I'm struggling to establish the identity below:
$\tan u (\csc u - \sin u) = \cos u$

Essence Ingram 2022-04-06

I'm trying to calculate below integral but I'm not able to do so:
$\int 120 \sqrt{2} \cdot \cos (2 π \cdot 60 t) d t = 120 \sqrt{2} \cdot \int \cos (2 π \cdot 60 t) d t$

Jewel Beard 2022-04-06

I'm trying to find the exact value of
$\int_{\frac{1}{\sqrt{3}}}^{\sqrt{3}} \frac{\arctan (x^{2})}{1 + x^{2}} d x$

Mina Whitehead 2022-04-06

I wonder how to solve this equation:
$\frac{\tan (x + 20^{\circ}) - \sin (x + 20^{\circ})}{\tan (x + 20^{\circ}) + \sin (x + 20^{\circ})}$

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